Publications

Abstract

Multi-antenna channel sounding is a technique for measuring the propagation characteristics of electromagnetic waves that is commonly employed for parameterizing channel models. Channel sounders are usually custom-built from many Software Defined Radio receivers, making them expensive to procure and difficult to operate, which constrains the set of users to a few specialized scientific institutions and industrial research laboratories. Recent developments in Joint Communications and Sensing (JCaS) extend the possible uses of channel data to applications like human activity recognition, human presence detection, user localization and wireless Channel Charting, all of which are of great interest to security researchers, experts in industrial automation and others. However, due to a lack of affordable, easy-to-use and commercially available multi-antenna channel sounders, those scientific communities can be hindered by their lack of access to wireless channel measurements. To lower the barrier to entry for channel sounding, we develop an ultra low-cost measurement hardware platform based on mass-produced WiFi chips, which is easily affordable to research groups and even hobbyists.

Abstract

We propose and practically demonstrate a joint detection and decoding scheme for short-packet wireless communications in scenarios that require to first detect the presence of a message before actually decoding it. For this, we extend the recently proposed serial Turbo-autoencoder neural network (NN) architecture and train it to find short messages that can be, all “at once”, detected, synchronized, equalized and decoded when sent over an unsynchronized channel with memory. The conceptional advantage of the proposed system stems from a holistic message structure with superimposed pilots for joint detection and decoding without the need of relying on a dedicated preamble. This results not only in a higher spectral efficiency, but also translates into the possibility of shorter messages compared to using a dedicated preamble. We compare the detection error rate (DER), bit error rate (BER) and block error rate (BLER) performance of the proposed system with a hand-crafted state-of-the-art conventional baseline and our simulations show a significant advantage of the proposed autoencoder-based system over the conventional baseline in every scenario up to messages conveying k =96 information bits. Finally, we practically evaluate and confirm the improved performance of the proposed system over-the-air (OTA) using a software-defined radio (SDR)-based measurement testbed.

Abstract

Future cellular networks are intended to have the ability to sense the environment by utilizing reflections of transmitted signals. Multi-dimensional sensing brings along the crucial advantage of being able to resort to multiple domains to resolve targets, enhancing detection capabilities compared to one-dimensional (1D) estimation. However, estimating parameters jointly in 5G New Radio systems poses the challenge of limiting the computational complexity while preserving a high resolution. To that end, we make use of channel state information (CSI) decimation for MUltiple SIgnal Classification (MUSIC)-based joint range-angle of arrival estimation. We further introduce multi-peak search routines to achieve additional detection capability improvements. Simulation results with orthogonal frequency-division multiplexing (OFDM) signals show that we attain higher detection probabilities for closely spaced targets than with 1D range-only estimation. Moreover, we demonstrate that for our considered 5G setup, we are able to significantly reduce the required number of computations due to CSI decimation.

Abstract

Permutation decoding gained recent interest as it can exploit the symmetries of a code in a parallel fashion. Moreover, it has been shown that by viewing permuted polar codes as polar subcodes, the set of usable permutations in permutation decoding can be increased. We extend this idea to pre-transformed polar codes, such as cyclic redundancy check (CRC)-aided polar codes, which previously could not be decoded using permutations due to their lack of automorphisms. Using belief propagation (BP)-based subdecoders, we showcase a performance close to CRC-aided SCL (CA-SCL) decoding. The proposed algorithm outperforms the previously best performing iterative CRC-aided belief propagation list (CA-BPL) decoder both in error-rate performance and decoding latency.

Abstract

We consider automorphism ensemble decoding (AED) of quasi-cyclic (QC) low-density parity-check (LDPC) codes. Belief propagation (BP) decoding on the conventional factor graph is equivariant to the quasi-cyclic automorphisms and therefore prevents gains by AED. However, by applying small modifications to the parity-check matrix at the receiver side, we can break the symmetry without changing the code at the transmitter. This way, we can leverage a gain in error-correcting performance using an ensemble of identical BP decoders, without increasing the worst-case decoding latency. The proposed method is demonstrated using LDPC codes from the CCSDS, 802.11n and 5G standards and produces gains of 0.2 to 0.3 dB over conventional BP decoding.

Abstract

When operating massive multiple-input multiple-output (MIMO) systems with uplink (UL) and downlink (DL) channels at different frequencies (frequency division duplex (FDD) operation), acquisition of channel state information (CSI) for downlink precoding is a major challenge. Since, barring transceiver impairments, both UL and DL CSI are determined by the physical environment surrounding transmitter and receiver, it stands to reason that, for a static environment, a mapping from UL CSI to DL CSI may exist. First, we propose to use various neural network (NN)-based approaches that learn this mapping and provide baselines using classical signal processing. Second, we introduce a scheme to evaluate the performance and quality of generalization of all approaches, distinguishing between known and previously unseen physical locations. Third, we evaluate all approaches on a real-world indoor dataset collected with a 32-antenna channel sounder.

Abstract

In communication systems, autoencoder refers to a system that replaces parts of the traditional transmitter and receiver of the baseband processing chain with artificial neural networks (ANNs). This allows to jointly train the system for an underlying channel model by reconstructing the input symbols at the output. Since the actual behavior of a real communication channel cannot be perfectly reproduced by an abstract model, it is necessary for the autoencoder to adapt to the changing conditions at runtime. Thus, online fine-tuning, in the form of ANN-retraining is of great importance. A platform able to satisfy the low-latency and low-power requirements of embedded communication systems are Field-programmable gate arrays (FPGAs). In this paper, we present an online-trainable low-power FPGA architecture for the receiver of an autoencoder-based communication chain. The architecture is embedded into an exploration framework that automatically determines the optimal degree of parallelism to minimize latency or power consumption. Our solutions achieve 2000×higher throughput than a high-performance GPU, draw 5×less power than an embedded CPU and are 5800×more energy efficient compared to an embedded GPU, for a batch size of one. To the best of our knowledge, this is the first FPGA-based autoencoder implementation for communication systems.

Abstract

Synchronization of transceiver chains is a major challenge in the practical realization of massive MIMO and especially distributed massive MIMO. While frequency synchronization is comparatively easy to achieve, estimating the carrier phase and sampling time offsets of individual transceivers is challenging. However, under the assumption of phase and time offsets that are constant over some duration and knowing the positions of several transmit and receive antennas, it is possible to estimate and compensate for these offsets even in scattering environments with multipath propagation components. The resulting phase and time calibration is a prerequisite for applying classical antenna array processing methods to massive MIMO arrays and for transferring machine learning models either between simulation and deployment or from one radio environment to another. Algorithms for phase and time offset estimation are presented and several investigations on large datasets generated by an over-the-air-synchronized channel sounder are carried out.

Abstract

We propose and practically demonstrate a joint detection and decoding scheme for short-packet wireless communications in scenarios that require to first detect the presence of a message before actually decoding it. For this, we extend the recently proposed serial Turbo-autoencoder neural network (NN) architecture and train it to find short messages that can be, all “at once”, detected, synchronized, equalized and decoded when sent over an unsynchronized channel with memory. The conceptional advantage of the proposed system stems from a holistic message structure with superimposed pilots for joint detection and decoding without the need of relying on a dedicated preamble. This results not only in a higher spectral efficiency, but also translates into the possibility of shorter messages compared to using a dedicated preamble. We compare the detection error rate (DER), bit error rate (BER) and block error rate (BLER) performance of the proposed system with a hand-crafted state-of-the-art conventional baseline and our simulations show a significant advantage of the proposed autoencoder-based system over the conventional baseline in every scenario up to messages conveying k =96 information bits. Finally, we practically evaluate and confirm the improved performance of the proposed system over-the-air (OTA) using a software-defined radio (SDR)-based measurement testbed.

Abstract

The continuously increasing bandwidth and antenna aperture available in wireless networks laid the foundation for developing competitive positioning solutions relying on communications standards and hardware. However, poor propagation conditions such as non-line of sight (NLOS) and rich multipath still pose many challenges due to outlier measurements that significantly degrade the positioning performance.In this work, we introduce an iterative positioning method that reweights the time of arrival (ToA) and angle of arrival (AoA) measurements originating from multiple locators in order to efficiently remove outliers. In contrast to existing approaches that typically rely on a single locator to set the time reference for the time difference of arrival (TDoA) measurements corresponding to the remaining locators, and whose measurements may be unreliable, the proposed iterative approach does not rely on a reference locator only. The resulting robust position estimate is then used to initialize a computationally efficient gradient search to perform maximum likelihood position estimation.Our proposal is validated with an experimental setup at 3.75 GHz with 5G numerology in an indoor factory scenario, achieving an error of less than 50 cm in 95% of the measurements. To the best of our knowledge, this paper describes the first proof of concept for 5G-based joint ToA and AoA localization.

Abstract

The surge of massive antenna arrays in wireless networks calls for the adoption of analog/hybrid array solutions, where multiple antenna elements are driven by a common radio front end to form a beam along a specific angle in order to maximize the beamforming gain. Many heuristics have been proposed to sample the angular domain by trading off between sampling overhead and angular scanning step size, where arbitrarily small angular step size is only attainable with infinite sampling overhead. In this work we show that, for uniform linear and rectangular arrays, loss-less reconstruction of the array's angular response at arbitrary angular precision is possible using finite number of samples without resorting to assumptions of angular sparsity. The proposed method, sampling and reconstructing angular domain (SARA), defines how many and which angles to be sampled and the corresponding reconstruction. This general solution to scan the angular domain can therefore be applied not only to beam acquisition and channel estimation, but also to radio imaging techniques, making it a candidate for future integrated sensing and communications (ISAC). We evaluate our proposal by numerical evaluations, which provide clear advantages versus the other considered baselines both in terms of angular reconstruction performance and computational complexity.

Abstract

A distributed massive MIMO channel sounder for acquiring large CSI datasets, dubbed DICHASUS, is presented. The measured data has potential applications in the study of different machine learning algorithms for user localization, JCAS, channel charting, enabling massive MIMO in FDD operation, and many others. The proposed channel sounder architecture is distinct from similar previous designs in that each individual single-antenna receiver is completely autonomous, enabling arbitrary grouping into spatially distributed antenna deployments, and offering virtually unlimited scalability in the number of antennas. Optionally, extracted channel coefficient vectors can be tagged with ground truth position data, obtained either through a GNSS receiver (for outdoor operation) or through various indoor positioning techniques.

Abstract

Reed—Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an open problem. In this work, we present a versatile decoding architecture for RM codes based on their rich automorphism group. The decoding algorithm can be seen as a generalization of multiple-bases belief propagation (MBBP) and may use any polar or RM decoder as constituent decoders. We provide extensive error-rate performance simulations for successive cancellation (SC)-, SC-list (SCL)-and belief propagation (BP)-based constituent decoders.We furthermore compare our results to existing decoding schemes and report a near-ML performance for the RM(3,7)-code (e.g., 0.04 dB away from the ML bound at BLER of 10–3) at a competitive computational cost. Moreover, we provide some insights into the automorphism subgroups of RM codes and SC decoding and, thereby, prove the theoretical limitations of this method with respect to polar codes.

Abstract

We propose an end-to-end learned bit-wise autoen-coder neural network (NN) for open loop multiple-input multiple-output (MIMO) antenna based communication systems. The optimized transmit vector constellations are learned based on the number of transmit and receive antennas, the number of bits conveyed per channel use and the signal-to-noise ratio. By training through an i.i.d. complex Gaussian (i.e., Rayleigh ergodic) matrix channel, the system implicitly picks up constellation shaping gains “along the way”. We evaluate and analyze these gains in comparison to the single-input single-output (SISO) results shown in 1 for different symmetric and asymmetric MIMO configurations. We first show that the NN-based receiver is able to compete with the a posteriori probability (APP) receiver performance up to certain configuration settings. Then we perform an end-to-end optimization of the transmit vector constellations using the conventional APP receiver as the decoder part. Thereby, we also investigate an edge case where the number of bits per vector symbol is not a multiple of the number of transmit antennas. Finally, we examine the performance of the system if a non-optimal zero forcing (ZF) receiver is used for inference, while the vector constellation was optimized for the APP receiver during training. We show that constellations optimized for the APP receiver are not necessarily optimal for such sub-optimal receivers that operate with reduced complexity. To fix this, we propose a detector-aware training scheme to learn constellations that have been optimized for a specific sub-optimal receiver and, thus, achieve higher performance in inference.

Abstract

Dual-containing classical error-correcting codes can be used in the Calderbank-Shor-Steane (CSS) construction for quantum error-correcting codes (QECCs). Dual-containing Bose-Chaudhuri-Hocquenghem (BCH) codes have been extensively studied in this regard. Research on the more general alternant codes is far less complete, despite the perspective of finding superior codes among them. In this paper, conditions for an alternant code to contain its Euclidean dual code are derived. The necessity of having dual-containing generalized Reed-Solomon (GRS) codes is shown and the structure of such codes is studied. An approach for constructing dual-containing alternant codes from BCH codes is proposed. In addition, a method for finding GRS codes over a given finite field with dual-containing alternant subfield-subcodes is presented. This method encompasses dual-containing BCH codes as a special case.

Abstract

Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an open problem. In this work, we present a belief propagation (BP) decoding architecture for RM codes based on their rich automorphism group. The decoding algorithm can be seen as a generalization of multiple-bases belief propagation (MBBP) using polar BP as constituent decoders. We provide extensive error-rate performance simulations and compare our results to existing decoding schemes. We report a near-ML performance for the RM(3,7)-code (e.g., 0.05 dB away from the ML bound at BLER of $10^-4$) at a competitive computational cost. To the best of our knowledge, our proposed decoder achieves the best performance of all iterative RM decoders presented thus far.

Abstract

Integrated Sensing And Communication (ISAC)forms a symbiosis between the human need for communication and the need for increasing productivity, by extracting environmental information leveraging the communication network. As multiple sensory already create a perception of the environment, an investigation into the advantages of ISAC compare to such modalities is required. Therefore, we introduce MaxRay, an ISAC framework allowing to simulate communication, sensing, and additional sensory jointly. Emphasizing the challenges for creating such sensing networks, we introduce the required propagation properties for sensing and how they are leveraged. To compare the performance of the different sensing techniques, we analyze four commonly used metrics used in different fields and evaluate their advantages and disadvantages for sensing. We depict that a metric based on prominence is suitable to cover most algorithms. Further we highlight the requirement of clutter removal algorithms, using two standard clutter removal techniques to detect a target in a typical industrial scenario. In general a versatile framework, allowing to create automatically labeled datasets to investigate a large variety of tasks is demonstrated.

Abstract

The automorphism group of a code is the set of permutations of the codeword symbols that map the whole code onto itself. For polar codes, only a part of the automorphism group was known, namely the lower-triangular affine group (LTA), which is solely based upon the partial order of the code's synthetic channels. Depending on the design, however, polar codes can have a richer set of automorphisms. In this paper, we extend the LTA to a larger subgroup of the general affine group (GA), namely the block lower-triangular affine group (BLTA) and show that it is contained in the automorphism group of polar codes. Furthermore, we provide a low complexity algorithm for finding this group for a given information/frozen set and determining its size. Most importantly, we apply these findings in automorphism-based decoding of polar codes and report a comparable error-rate performance to that of successive cancellation list (SCL) decoding with significantly lower complexity.

Abstract

Identifiers and sequence numbers make up a large part of the protocol overhead in certain low-power wide-area networks. The requirement for cryptographic nonces in au-thentication and encryption schemes often demands excessively long sequence numbers, which leads to an increase in energy consumption per transmitted packet. In this paper, the novelPERIDOT coding scheme is proposed. It replaces identifiers and sequence numbers with a code, based on which receivers can identify transmitters with high confidence. PERIDOT isbased on specially constructed integer permutations assigned to transmitters. An upper bound on the performance of PERIDOT codes is provided and methods for constructing particularlysuitable permutations are presented. In practice, PERIDOT can significantly increase intervals between nonce reuses and, at the same time, reduce power consumption.

Abstract

Attracted by its scalability towards practical codeword lengths, we revisit the idea of Turbo-autoencoders for end-to-end learning of PHY-Layer communications. For this, we study the existing concepts of Turbo-autoencoders from the literature and compare the concept with state-of-the-art classical coding schemes. We propose a new component-wise training algorithm based on the idea of Gaussian a priori distributions that reduces the overall training time by almost a magnitude. Further, we propose a new serial architecture inspired by classical serially concatenated Turbo code structures and show that a carefully optimized interface between the two component autoencoders is required. To the best of our knowledge, these serial Turbo autoencoder structures are the best known neural network based learned sequences that can be trained from scratch without any required expert knowledge in the domain of channel codes.

Abstract

We compare the potential of neural network (NN)-based channel estimation with classical linear minimum mean square error (LMMSE)-based estimators, also known as Wiener filtering. For this, we propose a low-complexity recurrent neural network (RNN)-based estimator that allows channel equalization of a sequence of channel observations based on independent time- and frequency-domain long short-term memory (LSTM) cells. Motivated by Vehicle-to-Everything (V2X) applications, we simulate time- and frequency-selective channels with orthogonal frequency division multiplex (OFDM) and extend our channel models in such a way that a continuous degradation from line-of-sight (LoS) to non-line-of-sight (NLoS) conditions can be emulated. It turns out that the NN-based system cannot just compete with the LMMSE equalizer, but it also can be trained w.r.t. resilience against system parameter mismatch. We thereby showcase the conceptual simplicity of such a data-driven system design, as this not only enables more robustness against, e.g., signal-to-noise-ratio (SNR) or Doppler spread estimation mismatches, but also allows to use the same equalizer over a wider range of input parameters without the need of re-building (or re-estimating) the filter coefficients. Particular attention has been paid to ensure compatibility with the existing IEEE 802.11p piloting scheme for V2X communications. Finally, feeding the payload data symbols as additional equalizer input unleashes further performance gains. We show significant gains over the conventional LMMSE equalization for highly dynamic channel conditions if such a data-augmented equalization scheme is used.

Abstract

Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an open problem. In this work, we present a versatile decoding architecture for RM codes based on their rich automorphism group. The decoding algorithm can be seen as a generalization of multiple-bases belief propagation (MBBP) and may use any polar or RM decoder as constituent decoders. We provide extensive error-rate performance simulations for successive cancellation (SC)-, SC-list (SCL)- and belief propagation (BP)-based constituent decoders. We furthermore compare our results to existing decoding schemes and report a near-ML performance for the RM(3,7)-code (e.g., 0.04 dB away from the ML bound at BLER of $10^-3$) at a competitive computational cost. Moreover, we provide some insights into the automorphism subgroups of RM codes and SC decoding and, thereby, prove the theoretical limitations of this method with respect to polar codes.

Abstract

Although iterative decoding of polar codes has recently made huge progress based on the idea of permuted factor graphs, it still suffers from a non-negligible performance degradation when compared to state-of-the-art CRC-aided successive cancellation list (CA-SCL) decoding. In this work, we show that iterative decoding of polar codes based on the belief propagation list (BPL) algorithm can approach the error-rate performance of CA-SCL decoding and, thus, can be efficiently used for decoding the standardized 5G polar codes. Rather than only utilizing the cyclic redundancy check (CRC) as a stopping condition (i.e., for error-detection), we also aim to benefit from the error-correction capabilities of the outer CRC code. For this, we develop two distinct soft-decision CRC decoding algorithms: a Bahl-Cocke-Jelinek-Raviv (BCJR)-based approach and a sum product algorithm (SPA)-based approach. Further, an optimized selection of permuted factor graphs is analyzed and shown to reduce the decoding complexity significantly. Finally, we benchmark the proposed CRC-aided belief propagation list (CA-BPL) decoding to state-of-the-art 5G polar codes under CA-SCL decoding and, thereby, showcase an error-rate performance not just close to the CA-SCL but also close to the maximum likelihood (ML) bound as estimated by ordered statistic decoding (OSD).

Abstract

Motivated by the recent success of end-to-end training of communications in the wireless domain, we strive to adapt the end-to-end-learning idea from the wireless case (i.e., linear) to coherent optical fiber links (i.e., nonlinear). Although, at first glance, it sounds like a straightforward extension, it turns out that several pitfalls exist – in terms of theory but also in terms of practical implementation. This paper analyzes an autoencoder’s potential and limitations for the optical fiber under the influence of Kerr-nonlinearity and chromatic dispersion. As there is no exact capacity limit known and, hence, no analytical perfect system solution available, we set great value to the interpretability on the learnings of the autoencoder. Therefore, we design its architecture to be as close as possible to the structure of a classic communication system, knowing that this may limit its degree of freedom and, thus, its performance. Nevertheless, we were able to achieve an unexpected high gain in terms of spectral efficiency compared to a conventional reference system.

Abstract

We consider the usage of finite-length polar codes for the Gaussian multiple access channel (GMAC) with a finite number of users. Based on the interleave-division multiple-access (IDMA) concept, we implement an iterative detection and decoding non-orthogonal multiple access (NOMA) receiver that benefits from a low complexity, while scaling (almost) linearly with the amount of active users. We further show the conceptual simplicity of the belief propagation (BP)-based decoder in a step-by-step illustration of its construction. Beyond its conceptual simplicity, this approach benefits from an improved performance when compared to some recent work tackling the same problem, namely the setup of finite-length forward error-correction (FEC) codes for finite-number of users. We consider the 5th generation mobile communication (5G) polar code with a block length N= 512 applied to both a two-user and a four-user GMAC scenario with a sum-rate of Rsum = 0.5 and Rsum = 1, respectively. Simulation results show that a BP-based soft interference cancellation (SoIC) receiver outperforms a joint successive cancellation (JSC) scheme. Finally, we investigate the effect of a concatenated repetition code which suggests that alternative polar code design rules are required in multi-user scenarios.

Abstract

In this paper we present a measurement set-up for massive MIMO channel sounding that shows very good long-term phase stability. Initial measurements were performed in a residential area to evaluate different conventional precoding schemes such as maximum ratio transmission and phase only precoding. A massive amount of data points was collected, with 924 times 64 complex channel weights per data point. Each data point is position-tagged using differential GPS with real-time kinematik, achieving better than 35cm position accuracy in more than 90% of the collected data points, making this dataset a rich resource for, e.g., further studying machine learning based, data-driven approaches in wireless communications.

Abstract

Massive MIMO uses a large number of antennas to increase the spectral efficiency (SE) through spatial multiplexing of users, which requires accurate channel state information. It is often assumed that regular pilots (RP), where a fraction of the time-frequency resources is reserved for pilots, suffices to provide high SE. However, the SE is limited by the pilot overhead and pilot contamination. An alternative is superimposed pilots (SP) where all resources are used for pilots and data. This removes the pilot overhead and reduces pilot contamination by using longer pilots. However, SP suffers from data interference that reduces the SE gains. This paper proposes the Massive-MIMO Iterative Channel Estimation and Decoding (MICED) algorithm where partially decoded data is used as side-information to improve the channel estimation and increase SE. We show that users with precise data estimates can help users with poor data estimates to decode. Numerical results with QPSK modulation and LDPC codes show that the MICED algorithm increases the SE and reduces the block-error-rate with RP and SP compared to conventional methods. The MICED algorithm with SP delivers the highest SE and it is especially effective in scenarios with short coherence blocks like high mobility or high frequencies.

Abstract

We consider a trainable point-to-point communication system, where both transmitter and receiver are implemented as neural networks (NNs), and demonstrate that training on the bit-wise mutual information (BMI) allows seamless integration with practical bit-metric decoding (BMD) receivers, as well as joint optimization of constellation shaping and labeling. Moreover, we present a fully differentiable neural iterative demapping and decoding (IDD) structure which achieves significant gains on additive white Gaussian noise (AWGN) channels using a standard 802.11n low-density parity-check (LDPC) code. The strength of this approach is that it can be applied to arbitrary channels without any modifications. Going one step further, we show that careful code design can lead to further performance improvements. Lastly, we show the viability of the proposed system through implementation on software-defined radios (SDRs) and training of the end-to-end system on the actual wireless channel. Experimental results reveal that the proposed method enables significant gains compared to conventional techniques.

Abstract

LDPC code design tools typically rely on asymptotic code behavior and are affected by an unavoidable performance degradation due to model imperfections in the short length regime. We propose an LDPC code design scheme based on an evolutionary algorithm, the Genetic Algorithm (GenAlg), implementing a “decoder-in-the-loop” concept. It inherently takes into consideration the channel, code length and the number of iterations while optimizing the error-rate of the actual decoder hardware architecture. We construct short length LDPC codes (i.e., the parity-check matrix) with error-rate performance comparable to, or even outperforming that of well-designed standardized short length LDPC codes over both AWGN and Rayleigh fading channels. Our proposed algorithm can be used to design LDPC codes with special graph structures (e.g., accumulator-based codes) to facilitate the encoding step, or to satisfy any other practical requirement. Moreover, GenAlg can be used to design LDPC codes with the aim of reducing decoding latency and complexity, leading to coding gains of up to 0.325 dB and 0.8 dB at BLER of 10-5 for both AWGN and Rayleigh fading channels, respectively, when compared to state-of-the-art short LDPC codes. Also, we analyze what can be learned from the resulting codes and, as such, the GenAlg particularly highlights design paradigms of short length LDPC codes (e.g., codes with degree-1 variable nodes obtain very good results).

Abstract

We present a new framework for constructing polar codes (i.e., selecting the frozen bit positions) for arbitrary channels, tailored to a given decoding algorithm rather than assuming the (not necessarily optimal) successive cancellation (SC) decoding. The proposed framework is based on the genetic algorithm (GenAlg), where populations (i.e., collections) of information sets evolve via evolutionary transformations based on their individual error-rate performance. These populations converge toward an information set that fits both the decoding behavior and the defined channel. We construct polar codes, without the CRC-aid, tailored to plain successive cancellation list (SCL) decoding, achieving the same error-rate performance as the CRC-aided SCL decoding over both the AWGN channel and the Rayleigh channel, respectively. Furthermore, a proposed belief propagation (BP)-tailored construction approaches the SCL error-rate performance without any modifications in the decoding algorithm itself. The performance gains can be attributed to the significant reduction in the number of low-weight codewords. We show that, when required, the GenAlg can also be set up to find codes that reduce the decoding complexity. This way, the SCL list size or the number of BP iterations can be reduced while maintaining the same error-rate performance.

Abstract

In this work, we introduce a deep learning-based polar code construction algorithm. The core idea is to represent the information/frozen bit indices of a polar code as a binary vector which can be interpreted as trainable weights of a neural network (NN). For this, we demonstrate how this binary vector can be relaxed to a soft-valued vector, facilitating the learning process through gradient descent and enabling an efficient code construction. We further show how different polar code design constraints (e.g., code rate) can be taken into account by means of careful binary-to-soft and soft-to-binary conversions, along with rate-adjustment after each learning iteration. Besides its conceptual simplicity, this approach benefits from having the “decoder-in-the-toop”, i.e., the nature of the decoder is inherently taken into consideration while learning (designing) the polar code. We show results for belief propagation (BP) decoding over both AWGN and Rayleigh fading channels with considerable performance gains over state-of-the-art construction schemes.

Abstract

We propose a new polar code construction framework (i.e., selecting the frozen bit positions) for the additive white Gaussian noise (AWGN) channel, tailored to a given decoding algorithm, rather than based on the (not necessarily optimal) assumption of successive cancellation (SC) decoding. The proposed framework is based on the Genetic Algorithm (GenAlg), where populations (i.e., collections) of information sets evolve successively via evolutionary transformations based on their individual error-rate performance. These populations converge towards an information set that fits the decoding behavior. Using our proposed algorithm, we construct a polar code of length 2048 with code rate 0.5, without the CRC-aid, tailored to plain successive cancellation list (SCL) decoding, achieving the same error-rate performance as the CRC-aided SCL decoding, and leading to a coding gain of 1dB at BER of 10(exp6). Further, a belief propagation (BP)-tailored polar code approaches the SCL error-rate performance without any modifications in the decoding algorithm itself.

Abstract

Iterative decoding of product codes constructed from constituent generalized Reed-Solomon codes (or subcodes thereof, such as Bose-Chaudhuri-Hocquenghem codes) is considered. In each iteration, the received symbols are updated according to horizontal and vertical decoding steps using a bounded distance decoder for the constituent codes. Symbols that were static for by a certain number of past iterations are considered trustworthy and it is assumed that they coincide with the originally transmitted codeword symbols. This enables list decoding of the constituent codes under partial codeword knowledge as proposed just recently. As a result, lower symbol error rates after decoding can be obtained.

Abstract

This paper considers the forward error correction (FEC) code design for approaching the capacity of a dynamic multiple access channel (MAC) where both the number of users and their respective signal powers keep constantly changing, resembling the scenario of an actual wireless cellular system. To obtain a low-complexity non-orthogonal multiple access (NOMA) scheme, we propose a serial concatenation of a low-density parity-check (LDPC) code and a repetition code (REP), this way achieving near Gaussian MAC (GMAC) capacity performance while coping with the dynamics of the MAC system. The joint optimization of the LDPC and REP codes is addressed by matching the analytical extrinsic information transfer (EXIT) functions of the sub-optimal multi-user detector (MUD) and the channel code for a specific and static MAC system, achieving near-GMAC capacity. We show that the near-capacity performance can be flexibly maintained with the same LDPC code regardless of the variations in the number of users and power levels. This flexibility (or elasticity) is provided by the REP code, acting as “user-load and power equalizer”, dramatically simplifying the practical implementation of NOMA schemes, as only a single LDPC code is needed to cope with the dynamics of the MAC system.

Abstract

With a significant increase in area throughput, Massive MIMO has become an enabling technology for fifth generation (5G) wireless mobile communication systems. Although prototypes were built, an openly available dataset for channel impulse responses to verify assumptions, e.g., regarding channel sparsity, is not yet available. In this paper, we introduce a novel channel sounder architecture capable of measuring multi-antenna and multi-subcarrier channel state information (CSI) at different frequency bands, antenna geometries and propagation environments. The channel sounder has been verified by evaluating channel data from first measurements. Such datasets can be used to study various deep-learning (DL) techniques in different applications, e.g., for indoor user positioning in three dimensions, as is done in this paper. Not only do we achieve an accuracy better than 75cm for line of sight (LoS), as is comparable to stateof-the-art conventional positioning techniques, but also obtain similar precision for the much more challenging case of non-line of sight (NLoS). Further extensive indoor/outdoor measurement campaigns will provide a more comprehensive open CSI dataset, tagged with positions, for the scientific community to further test various algorithms.

Abstract

List decoding of generalized Reed-Solomon codes is considered under the prerequisite that the transmitted codeword is partially known to the receiver. It is shown that this turns the standard noisy interpolation problem associated with the Guruswami-Sudan list decoder into a partially noisy and partially noise-free interpolation problem, which results in an improved error-correcting radius. It is further shown that the computational complexity of this approach is comparable to traditional bounded minimum distance decoding and that the only price for the exploitation of partial codeword knowledge is list size larger than one. In practice, partial codeword knowledge is available in decoding concatenated constructions such as staircase codes.

Abstract

In this work, we analyze the capabilities and practical limitations of neural networks (NNs) for sequence-based signal processing which can be seen as an omnipresent property in almost any modern communication systems. In particular, we train multiple state-of-the-art recurrent neural network (RNN) structures to learn how to decode convolutional codes allowing a clear benchmarking with the corresponding maximum likelihood (ML) Viterbi decoder. We examine the decoding performance for various kinds of NN architectures, beginning with classical types like feedforward layers and gated recurrent unit (GRU)-layers, up to more recently introduced architectures such as temporal convolutional networks (TCNs) and differentiable neural computers (DNCs) with external memory. As a key limitation, it turns out that the training complexity increases exponentially with the length of the encoding memory ν and, thus, practically limits the achievable bit error rate (BER) performance. To overcome this limitation, we introduce a new training-method by gradually increasing the number of ones within the training sequences, i.e., we constrain the amount of possible training sequences in the beginning until first convergence. By consecutively adding more and more possible sequences to the training set, we finally achieve training success in cases that did not converge before via naive training. Further, we show that our network can learn to jointly detect and decode a quadrature phase shift keying (QPSK) modulated code with sub-optimal (anti-Gray) labeling in one-shot at a performance that would require iterations between demapper and decoder in classic detection schemes.

Abstract

With a significant increase in data throughput, massive MIMO has become an enabling technology for fifth generation (5G) wireless mobile communication systems. Evaluating achievable throughputs in massive MIMO propagation environments using actual channel measurements is an important task. In this paper we characterize three measurement scenarios over four key channel parameters in typical urban environments. We show that different antenna geometries result in different dominating channel properties due to angular resolution and diversity, leading to antenna geometries favoring particular scenarios. A good compromise in antenna geometry is the unconventional "L"-structure for separating channels even in near proximity of the basestation. It is shown that the performance for a practical system in a Rician fading environment can be better approximated with the average K-factor and channel order Np

Abstract

We consider spatially coupled low-density parity-check (SC-LDPC) codes within a non-orthogonal interleave division multiple access (IDMA) scheme to avoid cumbersome degree profile matching of the LDPC code components to the iterative multi-user detector (MUD). Besides excellent decoding thresholds, the approach benefits from the possibility of using rather simple and regular underlying block LDPC codes owing to the universal behavior of the resulting coupled code with respect to the channel front-end, i.e., the iterative MUD. Furthermore, an additional outer repetition code makes the scheme flexible to cope with a varying number of users and user rates, as the SC-LDPC itself can be kept constant for a wide range of different user loads. The decoding thresholds are obtained via density evolution (DE) and verified by bit error rate (BER) simulations. To keep decoding complexity and latency small, we introduce a joint iterative windowed detector/decoder imposing carefully adjusted sub-block interleavers. Finally, we show that the proposed coding scheme also works for Rayleigh channels using the same code with tolerable performance loss compared to the additive white Gaussian noise (AWGN) channel.

Abstract

We analyze the achievable rates of time division duplex (TDD) and frequency division duplex (FDD) operations in massive MIMO systems depending on the coherence time and bandwidth of the underlying channel. In particular, an interlaced FDD (IFDD) scheme is considered due to both its simplicity and low pilot overhead. We establish the operational region of TDD and IFDD schemes for channels with different properties in the time and frequency domain. We prove that IFDD shall be preferred when the channel has large coherence bandwidth while TDD performs better if the channel has large coherence time. Furthermore, we evaluate the performance of TDD and IFDD systems for time-varying and frequency-selective channels via numerical simulations, showing that IFDD is an attractive alternative in high speed scenarios.

Abstract

A major obstacle for widespread deployment of frequency division duplex (FDD)-based massive multiple-input multiple-output (MIMO) communications is the large signaling overhead for reporting full downlink (DL) channel state information (CSI) back to the base station (BS), in order to enable closed-loop precoding. In this work, we practically demonstrate an FDD Massive MIMO system that avoids this overhead by employing a deep learning-driven channel extrapolation, i.e., a prediction of the CSI from one frequency to an adjacent frequency band. Further, we compare the resulting performance with other state-of-the-art extrapolation schemes and showcase significant advantages in complex propagation environments, e.g., caused by non-line-of-sight (NLoS) scenarios. Finally, we show, for actual (measured) channels, that a tailored neural network (NN) at the BS can infer DL CSI centered around a frequency f_DL by solely observing uplink (UL) CSI on a different, yet adjacent frequency band around f_UL , with only a small loss in spectral efficiency.

Abstract

We showcase the practicability of an indoor positioning system (IPS) solely based on neural networks (NNs) and the channel state information (CSI) of a (Massive) multiple-input multiple-output (MIMO) communication system, i.e., only build on the basis of data that is already existent in today's systems. As such our IPS system promises both, a good accuracy without the need of any additional protocol/signaling overhead for the user localization task. In particular, we propose a tailored NN structure with an additional phase branch as feature extractor and (compared to previous results) a significantly reduced amount of trainable parameters, leading to a minimization of the amount of required training data. We provide actual measurements for indoor scenarios with up to 64 antennas covering a large area of 80m2. In the second part, several robustness investigations for real-measurements are conducted, i.e., once trained, we analyze the recall accuracy over a period of several days. Further, we analyze the impact of pedestrians walking in-between the measurements and show that finetuning and pre-training of the NN helps to mitigate effects of hardware drifts and alterations in the propagation environment over time. This reduces the amount of required training samples at equal precision and, thereby, decreases the effort of the costly training data acquisition.

Abstract

We consider a trainable point-to-point communication system, where both transmitter and receiver are implemented as neural networks (NNs), and demonstrate that training on the bit-wise mutual information (BMI) allows seamless integration with practical bit-metric decoding (BMD) receivers, as well as joint optimization of constellation shaping and labeling. Moreover, we present a fully differentiable neural iterative demapping and decoding (IDD) structure which achieves significant gains on additive white Gaussian noise (AWGN) channels using a standard 802.11n low-density parity-check (LDPC) code. The strength of this approach is that it can be applied to arbitrary channels without any modifications. Going one step further, we show that careful code design can lead to further performance improvements. Lastly, we show the viability of the proposed system through implementation on software-defined radios (SDRs) and training of the end-to-end system on the actual wireless channel. Experimental results reveal that the proposed method enables significant gains compared to conventional techniques.

Abstract

The problem of finding subfield subcodes of generalized Reed-Solomon (GRS) codes (i.e., alternant codes) is considered. A pure linear algebraic approach is taken in order to derive message constraints that generalize the well known conjugacy constraints for cyclic GRS codes and their Bose-Chaudhuri-Hocquenghem (BCH) subfield subcodes. It is shown that the presented technique can be used for finding nested subfield subcodes with increasing design distance.

Abstract

Channel models for massive MIMO are typically based on matrices with complex Gaussian entries, extended by the Kronecker and Weichselberger model. One reason for observing a gap between modeled and actual channel behavior is the absence of spatial consistency in many such models, that is, spatial correlations over an area in the x; y-dimensions are not accounted for, making it difficult to study, e.g., area-throughput measures. In this paper, we propose an algorithm that can distinguish between regions of non-line-of-sight (NLoS) and lineof- sight (LoS) via a rank-metric criterion combined with a spiral search. With a k-means clustering algorithm a throughput per region (i.e., cluster) can be calculated, leading to what we refer to as ärea-throughput". For evaluating the proposed orthogonality clustering scheme we use a simple filtered MIMO channel model which is spatially consistent, with known degrees of freedom. Moreover, we employ actual (spatially consistent) area channel measurements based on spatial sampling using a spider antenna and show that the proposed algorithm can be used to estimate the degrees of freedom, and, subsequently, the number of users that maximizes the throughput per square meter.

Abstract

In this work, we analyze efficient window shift schemes for windowed decoding of spatially coupled low-density parity-check (SC-LDPC) codes, which is known to yield close-to-optimal decoding results when compared to full belief propagation (BP) decoding. However, a drawback of windowed decoding is that either a significant amount of window updates are required leading to unnecessary high decoding complexity or the decoder suffers from sporadic burst-like error patterns, causing a decoder stall. To tackle this effect and, thus, to reduce the average decoding complexity, the basic idea is to enable adaptive window shifts based on a bit error rate (BER) prediction, which reduces the amount of unnecessary updates. As the decoder stall does not occur in analytical investigations such as the density evolution (DE), we examine different schemes on a fixed test-set and exhaustive monte-carlo simulations based on our graphic processing unit (GPU) simulation framework. As a result, we can reduce the average decoding complexity of the naive windowed decoder while improving the BER performance when compared to a non-adaptive windowed decoding scheme. Furthermore, we show that a foresightful stall prediction does not significantly outperform a retrospective stall detection which is much easier to implement in practice.

Abstract

We show that the performance of iterative belief propagation (BP) decoding of polar codes can be enhanced by decoding over different carefully chosen factor graph realizations. With a genie-aided stopping condition, it can achieve the successive cancellation list (SCL) decoding performance which has already been shown to achieve the maximum likelihood (ML) bound provided that the list size is sufficiently large. The proposed decoder is based on different realizations of the polar code factor graph with randomly permuted stages during decoding. Additionally, a different way of visualizing the polar code factor graph is presented, facilitating the analysis of the underlying factor graph and the comparison of different graph permutations. In our proposed decoder, a high rate Cyclic Redundancy Check (CRC) code is concatenated with a polar code and used as an iteration stopping criterion (i.e., genie) to even outperform the SCL decoder of the plain polar code (without the CRC-aid). Although our permuted factor graph-based decoder does not outperform the SCL-CRC decoder, it achieves, to the best of our knowledge, the best performance of all iterative polar decoders presented thus far.

Abstract

We propose a belief propagation list (BPL) decoder with comparable performance to the successive cancellation list (SCL) decoder of polar codes, which already achieves the maximum likelihood (ML) bound of polar codes for sufficiently large list size L. The proposed decoder is composed of multiple parallel independent belief propagation (BP) decoders based on differently permuted polar code factor graphs. A list of possible transmitted codewords is generated and the one closest to the received vector, in terms of Euclidean distance, is picked. To the best of our knowledge, the proposed BPL decoder provides the best performance of plain polar codes under iterative decoding known so far. The proposed algorithm does not require any changes in the polar code structure itself, rendering the BPL into an alternative to the SCL decoder, equipped with a soft output capability enabling, e.g., iterative detection and decoding to further improve performance. Further benefits are the lower decoding latency than the SCL decoder and the possibility of high throughput implementations. Additionally, we show that a different selection strategy of frozen bit positions can further enhance the error-rate performance of the proposed decoder.

Abstract

End-to-end learning of communications systems is a fascinating novel concept that has so far only been validated by simulations for block-based transmissions. It allows learning of transmitter and receiver implementations as deep neural networks (NNs) that are optimized for an arbitrary differentiable end-to-end performance metric, e.g., block error rate (BLER). In this paper, we demonstrate that over-the-air transmissions are possible: We build, train, and run a complete communications system solely composed of NNs using unsynchronized off-the-shelf software-defined radios and open-source deep learning software libraries. We extend the existing ideas toward continuous data transmission, which eases their current restriction to short block lengths but also entails the issue of receiver synchronization. We overcome this problem by introducing a frame synchronization module based on another NN. A comparison of the BLER performance of the “learned” system with that of a practical baseline shows competitive performance close to 1 dB, even without extensive hyperparameter tuning. We identify several practical challenges of training such a system over actual channels, in particular, the missing channel gradient, and propose a two-step learning procedure based on the idea of transfer learning that circumvents this issue.

Abstract

End-to-end learning of communications systems is a fascinating novel concept that has so far only been validated by simulations for block-based transmissions. It allows learning of transmitter and receiver implementations as deep neural networks (NNs) that are optimized for an arbitrary differentiable end-to-end performance metric, e.g., block error rate (BLER). In this paper, we demonstrate that over-the-air transmissions are possible: We build, train, and run a complete communications system solely composed of NNs using unsynchronized off-the-shelf software-defined radios and open-source deep learning software libraries. We extend the existing ideas toward continuous data transmission, which eases their current restriction to short block lengths but also entails the issue of receiver synchronization. We overcome this problem by introducing a frame synchronization module based on another NN. A comparison of the BLER performance of the “learned” system with that of a practical baseline shows competitive performance close to 1 dB, even without extensive hyperparameter tuning. We identify several practical challenges of training such a system over actual channels, in particular, the missing channel gradient, and propose a two-step learning procedure based on the idea of transfer learning that circumvents this issue.

Abstract

We consider the design of low-density parity-check (LDPC) codes with close-to-capacity performance for interleave division multiple access (IDMA). The degree profile of the LDPC code is optimized using extrinsic information transfer (EXIT) charts to match an IDMA low complexity multiuser detector. Analytical EXIT functions for the IDMA system are derived while verifying that the Gaussian approximation stays valid for a sufficiently large number of users. The resulting LDPC codes are of rather low-rate (e.g., Rc = 0.03 for 32 users) and thus, the practical design of such codes is quite challenging and may, due to the low code-rate, not even yield a performance close to the Gaussian multiple access channel (GMAC) capacity. Adding a serial concatenation with a simple repetition code allows to design matching LDPC codes with a higher rate and, this way, achieving closer to GMAC capacity. This makes IDMA an attractive multiple access scheme for future wireless communication systems.

Abstract

We extend the idea of end-to-end learning of communications systems through deep neural network (NN)-based autoencoders to orthogonal frequency division multiplexing (OFDM) with cyclic prefix (CP). Our implementation has the same benefits as a conventional OFDM system, namely single-tap equalization and robustness against sampling synchronization errors, which turned out to be one of the major challenges in previous single-carrier implementations. This enables reliable communication over multipath channels and makes the communication scheme suitable for commodity hardware with imprecise oscillators. We show that the proposed scheme can be realized with state-of-the-art deep learning software libraries as transmitter and receiver solely consist of differentiable layers required for gradient-based training. We compare the performance of the autoencoder-based system against that of a state-of-the-art OFDM baseline over frequency-selective fading channels. Finally, the impact of a non-linear amplifier is investigated and we show that the autoencoder inherently learns how to deal with such hardware impairments.

Abstract

We extend the idea of end-to-end learning of communications systems through deep neural network (NN)-based autoencoders to orthogonal frequency division multiplexing (OFDM) with cyclic prefix (CP). Our implementation has the same benefits as a conventional OFDM system, namely single-tap equalization and robustness against sampling synchronization errors, which turned out to be one of the major challenges in previous single-carrier implementations. This enables reliable communication over multipath channels and makes the communication scheme suitable for commodity hardware with imprecise oscillators. We show that the proposed scheme can be realized with state-of-the-art deep learning software libraries as transmitter and receiver solely consist of differentiable layers required for gradient-based training. We compare the performance of the autoencoder-based system against that of a state-of-the-art OFDM baseline over frequency-selective fading channels. Finally, the impact of a non-linear amplifier is investigated and we show that the autoencoder inherently learns how to deal with such hardware impairments.

Abstract

We examine the usability of deep neural networks for multiple-input multiple-output (MIMO) user positioning solely based on the orthogonal frequency division multiplex (OFDM) complex channel coefficients. In contrast to other indoor positioning systems (IPSs), the proposed method does not require any additional piloting overhead or any other changes in the communications system itself as it is deployed on top of an existing OFDM MIMO system. Supported by actual measurements, we are mainly interested in the more challenging non-line of sight (NLoS) scenario. However, gradient descent optimization is known to require a large amount of data-points for training, i.e., the required database would be too large when compared to conventional methods. Thus, we propose a two-step training procedure, with training on simulated line of sight (LoS) data in the first step, and finetuning on measured NLoS positions in the second step. This turns out to reduce the required measured training positions and thus, reduces the effort for data acquisition.

Abstract

We examine the usability of deep neural networks for multiple-input multiple-output (MIMO) user positioning solely based on the orthogonal frequency division multiplex (OFDM) complex channel coefficients. In contrast to other indoor positioning systems (IPSs), the proposed method does not require any additional piloting overhead or any other changes in the communications system itself as it is deployed on top of an existing OFDM MIMO system. Supported by actual measurements, we are mainly interested in the more challenging non-line of sight (NLoS) scenario. However, gradient descent optimization is known to require a large amount of data-points for training, i.e., the required database would be too large when compared to conventional methods. Thus, we propose a two-step training procedure, with training on simulated line of sight (LoS) data in the first step, and finetuning on measured NLoS positions in the second step. This turns out to reduce the required measured training positions and thus, reduces the effort for data acquisition.

Abstract

We demonstrate that error correcting codes (ECCs) can be used to construct a labeled data set for finetuning of “trainable” communication systems without sacrificing resources for the transmission of known symbols. This enables adaptive systems, which can be trained on-the-fly to compensate for slow fluctuations in channel conditions or varying hardware impairments. We examine the influence of corrupted training data and show that it is crucial to train based on correct labels. The proposed method can be applied to fully end-to-end trained communication systems (autoencoders) as well as systems with only some trainable components. This is exemplified by extending a conventional OFDM system with a trainable pre-equalizer neural network (NN) that can be optimized at run time.

Abstract

We demonstrate that error correcting codes (ECCs) can be used to construct a labeled data set for finetuning of “trainable” communication systems without sacrificing resources for the transmission of known symbols. This enables adaptive systems, which can be trained on-the-fly to compensate for slow fluctuations in channel conditions or varying hardware impairments. We examine the influence of corrupted training data and show that it is crucial to train based on correct labels. The proposed method can be applied to fully end-to-end trained communication systems (autoencoders) as well as systems with only some trainable components. This is exemplified by extending a conventional OFDM system with a trainable pre-equalizer neural network (NN) that can be optimized at run time.

Abstract

We introduce the Scattered Extrinsic Information Transfer (S-EXIT) chart as a tool for optimizing degree profiles of short length Low-Density Parity-Check (LDPC) codes under iterative decoding. As degree profile optimization is typically done in the asymptotic length regime, there is space for further improvement when considering the finite length behavior. We propose to consider the average extrinsic information as a random variable, exploiting its specific distribution properties for guiding code design. We explain, step-by-step, how to generate an S-EXIT chart for short-length LDPC codes. We show that this approach achieves gains in terms of bit error rate (BER) of 0.5 dB and 0.6 dB over the additive white Gaussian noise (AWGN) channel for codeword lengths of 128 and 180 bits, respectively, at a target BER of 10-4 when compared to conventional Extrinsic Information Transfer (EXIT) chart-based optimization. Also, a performance gain for the Binary Erasure Channel (BEC) for a block (i.e., codeword) length of 180 bits is shown.

Abstract

We describe a novel approach to interpret a polar code as a low-density parity-check (LDPC)-like code with an underlying sparse decoding graph. This sparse graph is based on the encoding factor graph of polar codes and is suitable for conventional belief propagation (BP) decoding. We discuss several pruning techniques based on the check node decoder (CND) and variable node decoder (VND) update equations, significantly reducing the size (i.e., decoding complexity) of the parity-check matrix. As a result, iterative polar decoding can then be conducted on a sparse graph, akin to the traditional well-established LDPC decoding, e.g., using a fully parallel sum-product algorithm (SPA). This facilitates the systematic analysis and design of polar codes using the well-established tools known from analyzing LDPC codes. We show that the proposed iterative polar decoder has a negligible performance loss for short-to-intermediate codelengths compared to Arikan's original BP decoder. Finally, the proposed decoder is shown to benefit from both reduced complexity and reduced memory requirements and, thus, is more suitable for hardware implementations.

Abstract

Canonical Massive MIMO uses time division duplex (TDD) to exploit channel reciprocity within the coherence time, avoiding feedback of channel state information (CSI), as is required for precoding at the base station. We extend the idea of exploiting reciprocity to the coherence bandwidth, allocating subcarriers of a multicarrier (OFDM)-based system in an interlaced fashion to up- and downlink, respectively, referred to as (OFDM-)subcarrier interlaced FDD (IFDD). Exploiting this "two-dimensional" channel reciprocity within both time and frequency coherence does not require any CSI feedback and, even more so, offers faster-than-TDD channel tracking. To address imperfections of actual hardware, we conducted measurements, verifying the practical viability of IFDD. As it turns out, the scheme incurs similar transmit/receive isolation issues (self-interference) as well-known from the full-duplex (FDup) literature. As will be shown, such hardware challenges like self-interference or frequency offsets are not critical for massive MIMO operation, but can be neglected as the number of antennas grows large. Finally, we quantify how IFDD allows to track the channel variations much faster than TDD over a wide range of commonly used pilot symbol rates.

Abstract

It is shown that Tamo-Barg locally recoverable codes (LRCs) can be considered as subcodes of generalized Reed-Solomon (GRS) codes. Their encoding can be interpreted as sequential encoding with two particular constituent codes that depend on each other. The message constraint approach for finding subfield subcodes of GRS codes is transferred to this setting in order to obtain subfield subcodes of LRCs. The subcodes have the same locality as their parent codes, and at least their minimum distance.

Abstract

The decoding performance of polar codes strongly depends on the decoding algorithm used, while also the decoder throughput and its latency mainly depend on the decoding algorithm. In this work, we implement the powerful successive cancellation list (SCL) decoder on a GPU and identify the bottlenecks of this algorithm with respect to parallel computing and its difficulties. The inherent serial decoding property of the SCL algorithm naturally limits the achievable speed-up gains on GPUs when compared to CPU implementations. In order to increase the decoding throughput, we use a hybrid decoding scheme based on the belief propagation (BP) decoder, which can be intra- and inter-frame parallelized. The proposed scheme combines excellent decoding performance and high throughput within the signal-to-noise ratio (SNR) region of interest.

Abstract

Massive Multiple-Input Multiple-Output (MIMO) communications uses a large number of antennas at the base station to increase the data rate and user density in future wireless systems. For simulation, it has become common practice to use i.i.d. complex Gaussian matrix entries to obtain an average MIMO channel behavior. More refined models have been devised and proposed to standardization bodies; yet, channel modeling remains an active area of research, as current models tend to be, still, quite limited, e.g., when it comes to evaluating clustering algorithms, with regions of spatial orthogonality for concurrent scheduling of users, which is an essential concept in massive MIMO precoding. For this, spatial correlations need to be included. To further refine channel modeling, we have built a “spider antenna” prototype that allows spatially continuous measurements in three dimensions, enabling a high-resolution channel sampling over, initially, a volume of 2m × 2m × 2m for indoor measurements. Several experiments have been conducted to illustrate the new insights to be gained when studying user orthogonality, clustering and precoding in a massive MIMO context. Furthermore, the influence of antenna array geometry and user spacing on the achievable rate over actually measured channels is studied.

Abstract

The structure of polar codes inherently requires block lengths to be powers of two. In this paper, we investigate how different block lengths can be realized by coupling of several short-length polar codes. For this, we first analyze "code augmentation" to better protect the semipolarized channels, improving the BER performance under belief propagation decoding. Several serial and parallel augmentation schemes are discussed. A coding gain of 0:3 dB at a BER of 10(exp -5) can be observed for the same total rate and length. Further, we extend this approach towards coupling of several "sub-polar codes", leading to a reduced computational complexity and enabling the construction of flexible length polar codes.

Abstract

In this work, we show that polar belief propagation (BP) decoding exhibits an error floor behavior which is caused by clipping of the log-likelihood ratios (LLR). The error floor becomes more pronounced for clipping to smaller LLR-values. We introduce a single-value measure quantifying a “relative error floor”, showing, by exhaustive simulations for different lengths, that the error floor is mainly caused by inadequate clipping values. We propose four modifications to the conventional BP decoding algorithm to mitigate this error floor behavior, demonstrating that the error floor is a decoder property, and not a code property. The results agree with the fact that polar codes are theoretically proven to not suffer from error floors. Finally, we show that another cause of error floors can be an improper selection of frozen bit positions.

Abstract

We revisit the idea of using deep neural networks for one-shot decoding of random and structured codes, such as polar codes. Although it is possible to achieve maximum a posteriori (MAP) bit error rate (BER) performance for both code families and for short codeword lengths, we observe that (i) structured codes are easier to learn and (ii) the neural network is able to generalize to codewords that it has never seen during training for structured, but not for random codes. These results provide some evidence that neural networks can learn a form of decoding algorithm, rather than only a simple classifier. We introduce the metric normalized validation error (NVE) in order to further investigate the potential and limitations of deep learning-based decoding with respect to performance and complexity.

Abstract

In this work, we demonstrate an over-the-air communications system which is solely based on deep neural networks and has, thus far, only been validated by computer simulations for block-based transmissions. Transmitter and receiver can be jointly trained end-to-end for an arbitrary differentiable end-to-end performance metric, e.g., block error rate (BLER). We demonstrate that it is possible to build and train such a system using off-the-shelf software-defined radios (SDRs) and open-source deep learning software libraries. A comparison of the BLER performance of the "learned" system against that of a practical baseline shows competitive performance. We identify several practical challenges of training such a system over-the-air, in particular the missing channel gradient, and propose a learning procedure that circumvents this issue.

Abstract

The training complexity of deep learning-based channel decoders scales exponentially with the codebook size and therefore with the number of information bits. Thus, neural network decoding (NND) is currently only feasible for very short block lengths. In this work, we show that the conventional iterative decoding algorithm for polar codes can be enhanced when sub-blocks of the decoder are replaced by neural network (NN) based components. Thus, we partition the encoding graph into smaller sub-blocks and train them individually, closely approaching maximum a posteriori (MAP) performance per sub-block. These blocks are then connected via the remaining conventional belief propagation decoding stage(s). The resulting decoding algorithm is non-iterative and inherently enables a highlevel of parallelization, while showing a competitive bit error rate (BER) performance. We examine the degradation through partitioning and compare the resulting decoder to state-of-the art polar decoders such as successive cancellation list and belief propagation decoding.

Abstract

For finite length polar codes, channel polarization leaves a significant number of channels not fully polarized. Adding a Cyclic Redundancy Check (CRC) to better protect information on the semi-polarized channels has already been successfully applied in the literature, and is straightforward to be used in combination with Successive Cancellation List (SCL) decoding. Belief Propagation (BP) decoding, however, offers more potential for exploiting parallelism in hardware implementation, and thus, we focus our attention on improving the BP decoder. Specifically, similar to the CRC strategy in the SCL-case, we use a short-length “auxiliary” LDPC code together with the polar code to provide a significant improvement in terms of BER. We present the novel concept of “scattered” EXIT charts to design such auxiliary LDPC codes, and achieve net coding gains (i.e. for the same total rate) of 0.4dB at BER of 10-5 compared to the conventional BP decoder.

Abstract

A new interpretation of Bose-Chaudhuri-Hocquenghem codes is given, based on the imposition of certain conjugacy constraints on the message polynomials of their cyclic generalized Reed-Solomon (GRS) parent codes. This interpretation facilitates a merging of interpolation-based and syndrome-based decoders for GRS codes, resulting in syndrome-based decoders that do not require the computationally expensive Chien search and error evaluation steps.

Abstract

Spatially coupled low-density parity-check (SC-LDPC) codes can achieve the channel capacity under low-complexity belief propagation (BP) decoding, however, there is a non-negligible rate-loss because of termination effects for practical finite coupling lengths. In this paper, we study how we can approach the performance of terminated SC-LDPC codes by random shortening of tail-biting SC-LDPC codes. We find the minimum required rate-loss in order to achieve the same performance than terminated codes. We additionally study the use of tail-biting SC-LDPC codes for transmission over parallel channels (e.g., bit-interleaved-coded-modulation (BICM)) and investigate how the distribution of the coded bits between two parallel channels can change the performance of the code. We show that a tail-biting SC-LDPC code can be used with BP decoding almost anywhere within the achievable region of MAP decoding. The optimization comes with a mandatory buffer at the encoder side. We evaluate different distributions of coded bits in order to reduce this buffer length.

Abstract

For finite coupling lengths, terminated spatially coupled low-density parity-check (SC-LDPC) codes show a non-negligible rate-loss. In this paper, we investigate if this rate loss can be mitigated by tail-biting SC-LDPC codes in conjunction with iterative demapping of higher order modulation formats. Therefore, we examine the BP threshold of different coupled and uncoupled ensembles. A comparison between the decoding thresholds approximated by EXIT charts and the density evolution results of the coupled and uncoupled ensemble is given. We investigate the effect and potential of different labelings for such a set-up using per-bit EXIT curves, and exemplify the method for a 16-QAM system, e.g., using set partitioning labelings. A hybrid mapping is proposed, where different sub-blocks use different labelings in order to further optimize the decoding thresholds of tail-biting codes, while the computational complexity overhead through iterative demapping remains small.

Abstract

Sierpinski prefactors are introduced, a concept that exploits the fact that many binomial coefficients in the Hasse derivative that appears in the the Guruswami-Sudan interpolation step are zero modulo the field characteristic. A reduced Guruswami-Sudan interpolation step for generalized Reed-Solomon codes with significantly fewer unknowns than the original interpolation step is formulated.

Abstract

In the disproof of the Strong Simplex Conjecture presented in 1, a counterexample signal set was found that has higher average probability of correct optimal decoding than the corresponding regular simplex signal set, when compared at small values of the signal-to-noise ratio. The latter was defined as the quotient of average signal energy and average noise power. In this paper, it is shown that this interpretation of the signal-tonoise ratio is inappropriate for a comparison of signal sets, since it leads to a contradiction with the Channel Coding Theorem. A modified counterexample signal set is proposed and examined using the classical interpretation of the signal-to-noise ratio, i.e., as the quotient of average signal energy and average noise energy. This signal set outperforms the regular simplex signal set for small signal-to-noise ratios without contradicting the Channel Coding Theorem, hence the Strong Simplex Conjecture remains disproven.

Abstract

The Transmission Control Protocol (TCP) was designed for wired networks, where the probability of packet losses on the links is small. Modern variants of TCP provide reliable transport services for such networks, the Internet being the most prominent example. If either of the involved TCP instances of a transmission detects packet losses, it immediately reacts with a congestion avoidance technique like significantly decreasing the transmission window. Nowadays, the share of wireless links is growing steadily and the original TCP design assumption that all packet losses exclusively occur in routers due to congestion is not valid any more. As a result, the measurable performance (e.g. throughput, transmission round-trip time) of networks deteriorates if lossy wireless links are part of the transmission route. To cope with this flaw of the TCP design, a new network coding layer (NC layer) was proposed in Senger et al. 2010, which transparently sits in between the transport and network layers and hides non congestion-imposed packet losses from TCP. Our contribution is a framework which allows to adaptively switch between the main parameters of the NC layer (e.g. code rate). We show by simulation that the framework allows to improve measurable network performance for all practical non-zero packet loss probabilities.

Abstract

Generalized minimum distance (GMD) decoders allow for combining some virtues of probabilistic and algebraic decoding approaches at a low complexity. We investigate single-trial strategies for GMD decoding with arbitrary error-erasure tradeoff, based on either erasing a fraction of the received symbols or erasing all symbols whose reliability values are below a certain threshold. The fraction/threshold may be either static or adaptive, where adaptive means that the erasing is a function of the channel output. Adaptive erasing based on a threshold is a new technique that has not been investigated before. An asymptotic approach is used to evaluate the error-correction radius for each strategy. Both known and new results appear as special cases of this general framework.

Abstract

Many metrics used in coding theory are instances of a combinatorial metric introduced by Gabidulin. We define a weighted combinatorial semimetric. Some relations between these two metrics are established. Given an error and erasure decoder for the combinatorial metric, we propose the Forney-Kovalev soft-input-decoder for the weighted combinatorial metric. The error correcting radius of the algorithm is obtained for given number of decoding trials.

Abstract

We investigate adaptive single-trial error/erasure decoding of binary codes whose decoder is able to correct ε errors and τ erasures if λε + ≤ <; dmin -1. Thereby, dmin is the minimum Hamming distance and λ ϵ R, 1 <; λ <; 2, is the tradeoff parameter between errors and erasures. The error/erasure decoder allows to exploit soft information by treating a set of most unreliable received symbols as erasures. The obvious question here is, how this erasing should be performed, i.e. how the unreliable symbols that must be erased in order to obtain the smallest possible residual codeword error probability can be determined. This was answered before for the case of fixed erasing, where only the channel state and not the individual symbol reliabilities of each received vector are taken into consideration. In this paper, we address the adaptive case, where the optimal erasing strategy is determined for every given received vector.

Abstract

For decoding concatenated codes up to half their designed distance, generalized minimum distance (GMD) decoding can be used. GMD decoding applies multitrial error/erasure decoding of the outer code, where erased symbols depend on some reliability measure stemming from the inner decoders. We consider the case where the outer decoder is able to decode beyond half the minimum distance of the outer code. For a given number of outer decoding trials, we derive achievable decoding radii for GMD decoding. Vice versa, we give a lower bound on the number of required outer decoding trials to obtain the greatest possible decoding radius.

Abstract

We consider the Additive White Gaussian Noise channel with Binary Phase Shift Keying modulation. Our aim is to enable an algebraic hard decision Bounded Minimum Distance decoder for a binary block code to exploit soft information obtained from the demodulator. This idea goes back to Forney and is based on treating received symbols with low reliability as erasures. This erasing at the decoder is done using a threshold, each received symbol with reliability falling below the threshold is erased. Depending on the target overall complexity of the decoder this pseudo-soft decision decoding can be extended from one threshold T to z&#62;1 thresholds T_1&#60;...&#60;T_z for erasing received symbols with lowest reliability. The resulting technique is widely known as Generalized Minimum Distance decoding. In this paper we provide a means for explicit determination of the optimal threshold locations in terms of minimal decoding error probability. We do this for the one and the general z&#62;1 thresholds case, starting with a geometric interpretation of the optimal threshold location problem and using an approach from Zyablov.

Abstract

Generalized Concatenated codes are a code construction consisting of a number of outer codes whose code symbols are protected by an inner code. As outer codes, we assume the most frequently used Reed-Solomon codes; as inner code, we assume some linear block code which can be decoded up to half its minimum distance. Decoding up to half the minimum distance of Generalized Concatenated codes is classically achieved by the Blokh-Zyablov-Dumer algorithm, which iteratively decodes by first using the inner decoder to get an estimate of the outer code words and then using an outer error/erasure decoder with a varying number of erasures determined by a set of pre- calculated thresholds. In this paper, a modified version of the Blokh-Zyablov-Dumer algorithm is proposed, which exploits the fact that a number of outer Reed-Solomon codes with average minimum distance d macr can be grouped into one single Interleaved Reed-Solomon code which can be decoded beyond d macr/2. This allows to skip a number of decoding iterations on the one hand and to reduce the complexity of each decoding iteration significantly - while maintaining the decoding performance - on the other.

Abstract

This paper investigates q-cyclic Rank Codes, which are a subclass of codes with maximum rank distance. These codes are the analogon for the rank metric to cyclic Reed-Solomon codes for the Hamming metric. Similar to Reed-Solomon codes we define a discrete Fourier transform and its inverse for these codes. Furthermore, we show how to efficiently decode q-cyclic Rank Codes by making use of the discrete Fourier transform.