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Senger, Christian

Christian Senger

Dr.-Ing.

Deputy Director
Institute of Telecommunications

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+49 711 685 67942
+49 711 685 57942
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Pfaffenwaldring 47
70569 Stuttgart
Deutschland
Room: 2.345

Subject

My research interests focus on digital communications in general and error control coding in particular. I am generally attracted by everyday problems that can be tackled by applied math. Error control codes are certainly one of the most beautiful and practically relevant intersections between mathematics and engineering. I am sure that nobody can escape the fascination of building practical systems — based on finite fields as manageable surrogates for the real and complex numbers — that can cope with the inherent imperfectness of physical transmission channels.

Most of my studies, work, and research so far have been centered around digital communications, error control coding, and networks. These fields have already given us smart mobile phones, the Internet, and worldwide accessible cloud data storage; I believe that they still have the potential to further improve our daily experience with telecommunications and data handling. Besides the aforementioned main areas, I also reach out to fields such as information theory, cryptography, FPGA design, data storage systems, flash memories, and cellular automata in order to discover new applications and to reveal unsolved problems. I am interested in the whole chain of research; that is, understanding the mathematical foundations and physical constraints, designing and optimizing algorithms, and eventually working out new applications and products.

My current research interests are:

Error control coding
- Codes for fiber-optical high-speed networks
- Codes for distributed data storage
- Codes for flash memories
- Efficient VLSI implementations
Digital communications
Telecommunications systems, networking
Embedded security

Publications

2021
1. C. Senger, “CRC error detection for CAN XL,” in 17th international CAN Conference (iCC), Baden-Baden, Germany, 2021.
  - Abstract
  - BibTeX
  Abstract
  In this paper, CRC generator polynomials for detection of transmission errors in headers and frames of the upcoming CAN XL standard are proposed. Their properties, which are chosen such as to provide state of the art error detection performance (compared to competing standards) in the CAN XL scenario, are described. These properties include achieving Hamming distance six for the full range of possible message lengths. At the beginning of the paper, a self-contained recap of CRC codes is given.
  BibTeX
  @inproceedings{senger2020error, abstract = {In this paper, CRC generator polynomials for detection of transmission errors in headers and frames of the upcoming CAN XL standard are proposed. Their properties, which are chosen such as to provide state of the art error detection performance (compared to competing standards) in the CAN XL scenario, are described. These properties include achieving Hamming distance six for the full range of possible message lengths. At the beginning of the paper, a self-contained recap of CRC codes is given.}, author = {Senger, Christian}, booktitle = {17th international CAN Conference (iCC)}, publisher = {CAN in Automation (CiA)}, title = {CRC error detection for CAN XL}, venue = {Baden-Baden, Germany}, year = 2021 }
2. S. Miao and C. Senger, “Dual-containing Alternant Codes for Applications in the Calderbank-Shor-Steane Construction,” in 2021 IEEE International Symposium on Information Theory (ISIT), Melbourne, Australia, 2021, pp. 12–20.
  - Abstract
  - BibTeX
  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.
  BibTeX
  @inproceedings{miao2021dualcontaining, 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.}, author = {Miao, Sisi and Senger, Christian}, booktitle = {2021 IEEE International Symposium on Information Theory (ISIT)}, month = {07}, pages = {12-20}, title = {Dual-containing Alternant Codes for Applications in the Calderbank-Shor-Steane Construction}, venue = {Melbourne, Australia}, year = 2021 }
3. F. Euchner and C. Senger, “PERIDOT Codes: Replacing Identifiers, Sequence Numbers and Nonces with Permutations,” in 30th Biennial Symposium on Communications (BSC 2021), Saskatoon, SK, Canada, 2021.
  - Abstract
  - BibTeX
  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.
  BibTeX
  @inproceedings{euchner2021, 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.}, author = {Euchner, Florian and Senger, Christian}, booktitle = {30th Biennial Symposium on Communications (BSC 2021)}, title = {PERIDOT Codes: Replacing Identifiers, Sequence Numbers and Nonces with Permutations}, venue = {Saskatoon, SK, Canada}, year = 2021 }
2019
1. C. Senger, “Improved Iterative Decoding of Product Codes Based on Trusted Symbols,” in 2019 IEEE International Symposium on Information Theory (ISIT), 2019, pp. 1342–1346 [Online]. Available: https://ieeexplore.ieee.org/document/8849469
  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.
  BibTeX
  @inproceedings{8849469, 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.}, author = {{Senger}, C.}, booktitle = {2019 IEEE International Symposium on Information Theory (ISIT)}, doi = {10.1109/ISIT.2019.8849469}, issn = {2157-8095}, month = {07}, pages = {1342-1346}, title = {Improved Iterative Decoding of Product Codes Based on Trusted Symbols}, url = {https://ieeexplore.ieee.org/document/8849469}, year = 2019 }
  Link
  https://ieeexplore.ieee.org/document/8849469
2. C. Senger, “On List Decoding of Generalized Reed-Solomon Codes Under Partial Codeword Knowledge,” in SCC 2019; 12th International ITG Conference on Systems, Communications and Coding, 2019, pp. 1–5 [Online]. Available: https://ieeexplore.ieee.org/document/8661300
  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.
  BibTeX
  @inproceedings{8661300, 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.}, author = {{Senger}, C.}, booktitle = {SCC 2019; 12th International ITG Conference on Systems, Communications and Coding}, doi = {10.30420/454862003}, issn = {null}, month = {02}, pages = {1-5}, title = {On List Decoding of Generalized Reed-Solomon Codes Under Partial Codeword Knowledge}, url = {https://ieeexplore.ieee.org/document/8661300}, year = 2019 }
  Link
  https://ieeexplore.ieee.org/document/8661300
2018
1. C. Senger and R. Bohara, “A Linear Algebraic Approach to Subfield Subcodes of GRS Codes,” in 2018 IEEE International Symposium on Information Theory (ISIT), 2018, pp. 6–10 [Online]. Available: https://ieeexplore.ieee.org/document/8437645
  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.
  BibTeX
  @inproceedings{8437645, 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.}, author = {{Senger}, C. and {Bohara}, R.}, booktitle = {2018 IEEE International Symposium on Information Theory (ISIT)}, doi = {10.1109/ISIT.2018.8437645}, issn = {2157-8117}, month = {06}, pages = {6-10}, title = {A Linear Algebraic Approach to Subfield Subcodes of GRS Codes}, url = {https://ieeexplore.ieee.org/document/8437645}, year = 2018 }
  Link
  https://ieeexplore.ieee.org/document/8437645
2. C. Senger and H. K. Shivakumar, “Subfield Subcodes of Tamo–Barg Locally Recoverable Codes,” in 2018 29th Biennial Symposium on Communications (BSC), 2018, pp. 1–5 [Online]. Available: https://ieeexplore.ieee.org/document/8494698
  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.
  BibTeX
  @inproceedings{8494698, 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.}, author = {{Senger}, C. and {Shivakumar}, H. K.}, booktitle = {2018 29th Biennial Symposium on Communications (BSC)}, doi = {10.1109/BSC.2018.8494698}, issn = {null}, month = {06}, pages = {1-5}, title = {Subfield Subcodes of Tamo–Barg Locally Recoverable Codes}, url = {https://ieeexplore.ieee.org/document/8494698}, year = 2018 }
  Link
  https://ieeexplore.ieee.org/document/8494698
2016
1. C. Senger and F. R. Kschischang, “Syndrome-based Decoding of Evaluation Codes without Chien Search,” in 28th Biennial Symposium on Communications (BSC 2016), Kelowna, BC, Canada, 2016.
  - Abstract
  - BibTeX
  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.
  BibTeX
  @inproceedings{ref28, 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.}, address = {Kelowna, BC, Canada}, author = {Senger, Christian and Kschischang, Frank R}, booktitle = {28th Biennial Symposium on Communications (BSC 2016)}, title = {Syndrome-based Decoding of Evaluation Codes without Chien Search}, year = 2016 }
2014
1. C. Senger, V. Sidorenko, and A. Chaaban, “On multi-trial Forney-Kovalev decoding of concatenated codes,” Advances in Mathematics of Communications, vol. 8, no. 1, pp. 1--20, Jan. 2014 [Online]. Available: https://doi.org/10.3934%2Famc.2014.8.1
  - BibTeX
  - Link
  BibTeX
  @article{Senger_2014, author = {Senger, Christian and Sidorenko, Vladimir and Chaaban, Anas}, doi = {10.3934/amc.2014.8.1}, journal = {Advances in Mathematics of Communications}, month = {01}, number = 1, pages = {1--20}, publisher = {American Institute of Mathematical Sciences ({AIMS})}, title = {On multi-trial Forney-Kovalev decoding of concatenated codes}, url = {https://doi.org/10.3934%2Famc.2014.8.1}, volume = 8, year = 2014 }
  Link
  https://doi.org/10.3934%2Famc.2014.8.1
2. C. Senger, “Prefactor Reduction of the Guruswami–Sudan Interpolation Step,” IEEE Transactions on Information Theory, vol. 60, no. 12, pp. 7451–7463, Dec. 2014 [Online]. Available: https://ieeexplore.ieee.org/document/6915864
  Abstract
  The most computationally intensive step of the Guruswami-Sudan list decoder for generalized Reed-Solomon codes is the formation of a bivariate interpolation polynomial. Complexity can be reduced if this polynomial has prefactors, i.e., factors of its univariate constituent polynomials that are independent of the received vector, and hence known a priori. For example, the well-known re-encoding projection due to Koetter et al. leads to one class of prefactors. This paper introduces so-called Sierpínski prefactors that result from the property that many binomial coefficients, which arise in the multiplicity constraints defined in terms of the Hasse derivative, are zero modulo the underlying field characteristic. It is shown that re-encoding prefactors and Sierpínski prefactors can be combined to achieve a significantly reduced Guruswami-Sudan interpolation step. In certain practically relevant cases, the introduction of Sierpínski prefactors reduces the number of unknown polynomial coefficients by an additional 10% or more (beyond the reduction due to re-encoding prefactors alone), without incurring additional computational effort at the decoder.
  BibTeX
  @article{6915864, abstract = {The most computationally intensive step of the Guruswami-Sudan list decoder for generalized Reed-Solomon codes is the formation of a bivariate interpolation polynomial. Complexity can be reduced if this polynomial has prefactors, i.e., factors of its univariate constituent polynomials that are independent of the received vector, and hence known a priori. For example, the well-known re-encoding projection due to Koetter et al. leads to one class of prefactors. This paper introduces so-called Sierpínski prefactors that result from the property that many binomial coefficients, which arise in the multiplicity constraints defined in terms of the Hasse derivative, are zero modulo the underlying field characteristic. It is shown that re-encoding prefactors and Sierpínski prefactors can be combined to achieve a significantly reduced Guruswami-Sudan interpolation step. In certain practically relevant cases, the introduction of Sierpínski prefactors reduces the number of unknown polynomial coefficients by an additional 10% or more (beyond the reduction due to re-encoding prefactors alone), without incurring additional computational effort at the decoder.}, author = {{Senger}, C.}, doi = {10.1109/TIT.2014.2361347}, issn = {1557-9654}, journal = {IEEE Transactions on Information Theory}, month = {12}, number = 12, pages = {7451-7463}, title = {Prefactor Reduction of the Guruswami–Sudan Interpolation Step}, url = {https://ieeexplore.ieee.org/document/6915864}, volume = 60, year = 2014 }
  Link
  https://ieeexplore.ieee.org/document/6915864
3. C. Senger, “Sierpinski Prefactors in the Guruwami-Sudan Interpolation Step,” in 2014 International Zurich Seminar on Communications, Zurich, Switzerland, 2014, pp. 83–86 [Online]. Available: http://e-collection.library.ethz.ch/eserv/eth:8192/eth-8192-01.pdf
  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.
  BibTeX
  @inproceedings{ref24, 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.}, address = {Zurich, Switzerland}, author = {Senger, Christian}, booktitle = {2014 International Zurich Seminar on Communications}, doi = {10.3929/ethz-a-010089041}, pages = {83-86}, title = {Sierpinski Prefactors in the Guruwami-Sudan Interpolation Step}, url = {http://e-collection.library.ethz.ch/eserv/eth:8192/eth-8192-01.pdf}, year = 2014 }
  Link
  http://e-collection.library.ethz.ch/eserv/eth:8192/eth-8192-01.pdf
2013
1. D. E. Lazich, C. Senger, and M. Bossert, “A Corrected Disproof of the Strong Simplex Conjecture,” in SCC 2013; 9th International ITG Conference on Systems, Communication and Coding, 2013, pp. 1–5 [Online]. Available: https://ieeexplore.ieee.org/document/6469334
  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.
  BibTeX
  @inproceedings{6469334, 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.}, author = {{Lazich}, D. E. and {Senger}, C. and {Bossert}, M.}, booktitle = {SCC 2013; 9th International ITG Conference on Systems, Communication and Coding}, issn = {null}, month = {01}, pages = {1-5}, title = {A Corrected Disproof of the Strong Simplex Conjecture}, url = {https://ieeexplore.ieee.org/document/6469334}, year = 2013 }
  Link
  https://ieeexplore.ieee.org/document/6469334
2012
1. C. Senger, A. Zeh, Y. Fan, and S. Schober, “Adaptive End-to-End Network Coding based on Algebraic Codes,” in First International Workshop on Performance Evaluation and Modeling in Wireless Networks (PEMWN2012), Tunis, Tunisia, 2012.
  - Abstract
  - BibTeX
  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.
  BibTeX
  @inproceedings{ref22, 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.}, address = {Tunis, Tunisia}, author = {Senger, Christian and Zeh, Alexander and Fan, Yu and Schober, Steffen}, booktitle = {First International Workshop on Performance Evaluation and Modeling in Wireless Networks (PEMWN2012)}, title = {Adaptive End-to-End Network Coding based on Algebraic Codes}, year = 2012 }
2. J. H. Weber, V. R. Sidorenko, C. Senger, and K. A. S. Abdel-Ghaffar, “Asymptotic single-trial strategies for GMD decoding with arbitrary error-erasure tradeoff,” Problems of Information Transmission, vol. 48, no. 4, pp. 324--333, Oct. 2012 [Online]. Available: https://doi.org/10.1134/S0032946012040023
  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.
  BibTeX
  @article{Weber2012, 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.}, author = {Weber, J. H. and Sidorenko, V. R. and Senger, C. and Abdel-Ghaffar, K. A. S.}, day = 01, doi = {10.1134/S0032946012040023}, issn = {1608-3253}, journal = {Problems of Information Transmission}, month = {10}, number = 4, pages = {324--333}, title = {Asymptotic single-trial strategies for GMD decoding with arbitrary error-erasure tradeoff}, url = {https://doi.org/10.1134/S0032946012040023}, volume = 48, year = 2012 }
  Link
  https://doi.org/10.1134/S0032946012040023
2011
1. V. R. Sidorenko, C. Senger, and M. Bossert, “Decoding in Weighted Combinatorial Metric,” in International Mathematical Conference “50 Years of IPPI,” Moscow, Russia, 2011.
  - Abstract
  - BibTeX
  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.
  BibTeX
  @inproceedings{ref6, 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.}, address = {Moscow, Russia}, author = {Sidorenko, Vladimir R and Senger, Christian and Bossert, Martin}, booktitle = {International Mathematical Conference "50 Years of IPPI"}, title = {Decoding in Weighted Combinatorial Metric}, year = 2011 }
2010
1. C. Senger, V. R. Sidorenko, S. Schober, M. Bossert, and V. V. Zyablov, “Adaptive single-trial error/erasure decoding of binary codes,” in 2010 International Symposium On Information Theory Its Applications, 2010, pp. 267–272 [Online]. Available: https://ieeexplore.ieee.org/document/5648959
  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.
  BibTeX
  @inproceedings{5648959, 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.}, author = {{Senger}, C. and {Sidorenko}, V. R. and {Schober}, S. and {Bossert}, M. and {Zyablov}, V. V.}, booktitle = {2010 International Symposium On Information Theory Its Applications}, doi = {10.1109/ISITA.2010.5648959}, issn = {null}, month = {10}, pages = {267-272}, title = {Adaptive single-trial error/erasure decoding of binary codes}, url = {https://ieeexplore.ieee.org/document/5648959}, year = 2010 }
  Link
  https://ieeexplore.ieee.org/document/5648959
2. C. Senger, V. R. Sidorenko, M. Bossert, and V. V. Zyablov, “Multitrial decoding of concatenated codes using fixed thresholds,” Problems of Information Transmission, vol. 46, no. 2, pp. 127--141, Jun. 2010 [Online]. Available: https://doi.org/10.1134/S0032946010020031
  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.
  BibTeX
  @article{Senger2010, 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.}, author = {Senger, C. and Sidorenko, V. R. and Bossert, M. and Zyablov, V. V.}, day = 01, doi = {10.1134/S0032946010020031}, issn = {1608-3253}, journal = {Problems of Information Transmission}, month = {06}, number = 2, pages = {127--141}, title = {Multitrial decoding of concatenated codes using fixed thresholds}, url = {https://doi.org/10.1134/S0032946010020031}, volume = 46, year = 2010 }
  Link
  https://doi.org/10.1134/S0032946010020031
3. V. Sidorenko, and Christian Senger, M. Bossert, and V. Zyablov, “Single-trial decoding of concatenated codes using fixed or adaptive erasing,” Advances in Mathematics of Communications, vol. 4, no. 1, pp. 49--60, 2010 [Online]. Available: https://doi.org/10.3934%2Famc.2010.4.49
  - BibTeX
  - Link
  BibTeX
  @article{Sidorenko_2010, author = {Sidorenko, Vladimir and and Christian Senger and Bossert, Martin and Zyablov, Victor}, doi = {10.3934/amc.2010.4.49}, journal = {Advances in Mathematics of Communications}, number = 1, pages = {49--60}, publisher = {American Institute of Mathematical Sciences ({AIMS})}, title = {Single-trial decoding of concatenated codes using fixed or adaptive erasing}, url = {https://doi.org/10.3934%2Famc.2010.4.49}, volume = 4, year = 2010 }
  Link
  https://doi.org/10.3934%2Famc.2010.4.49
2009
1. C. Senger, V. R. Sidorenko, and V. V. Zyablov, “On Generalized Minimum Distance Decoding Thresholds for the AWGN Channel,” in XII International Symposium on Problems of Redundancy in Information and Control Systems, St. Petersburg, Russia, 2009, pp. 155–163.
  - Abstract
  - BibTeX
  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>1 thresholds T_1<...<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>1 thresholds case, starting with a geometric interpretation of the optimal threshold location problem and using an approach from Zyablov.
  BibTeX
  @inproceedings{ref15, 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>1 thresholds T_1<...<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>1 thresholds case, starting with a geometric interpretation of the optimal threshold location problem and using an approach from Zyablov. }, address = {St. Petersburg, Russia}, author = {Senger, Christian and Sidorenko, Vladimir R and Zyablov, Victor V}, booktitle = {XII International Symposium on Problems of Redundancy in Information and Control Systems}, pages = {155 - 163}, title = {On Generalized Minimum Distance Decoding Thresholds for the AWGN Channel}, urllink = {http://arxiv.org/abs/0903.3204}, year = 2009 }
2. C. Senger, “Optimized Error/Erasure Bounded Minimum Distance Decoding for the AWGN Channel,” in IEEE Information Theory Winter School 2009, Loen, Norway, 2009.
  - BibTeX
  BibTeX
  @inproceedings{ref16, address = {Loen, Norway}, author = {Senger, Christian}, booktitle = {IEEE Information Theory Winter School 2009}, title = {Optimized Error/Erasure Bounded Minimum Distance Decoding for the AWGN Channel}, year = 2009 }
2008
1. C. Senger, V. Sidorenko, M. Bossert, and V. Zyablov, “Decoding generalized concatenated codes using Interleaved Reed-Solomon codes,” in 2008 IEEE International Symposium on Information Theory, 2008, pp. 1808–1812 [Online]. Available: https://ieeexplore.ieee.org/document/4595300
  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.
  BibTeX
  @inproceedings{4595300, 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.}, author = {{Senger}, C. and {Sidorenko}, V. and {Bossert}, M. and {Zyablov}, V.}, booktitle = {2008 IEEE International Symposium on Information Theory}, doi = {10.1109/ISIT.2008.4595300}, issn = {2157-8117}, month = {07}, pages = {1808-1812}, title = {Decoding generalized concatenated codes using Interleaved Reed-Solomon codes}, url = {https://ieeexplore.ieee.org/document/4595300}, year = 2008 }
  Link
  https://ieeexplore.ieee.org/document/4595300
2. G. Richter, C. Senger, and M. Bossert, “Description and Decoding of q-cyclic Rank Codes,” in 7th International ITG Conference on Source and Channel Coding, 2008, pp. 1–6 [Online]. Available: https://ieeexplore.ieee.org/document/5755959
  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.
  BibTeX
  @inproceedings{5755959, 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.}, author = {{Richter}, G. and {Senger}, C. and {Bossert}, M.}, booktitle = {7th International ITG Conference on Source and Channel Coding}, issn = {null}, month = {01}, pages = {1-6}, title = {Description and Decoding of q-cyclic Rank Codes}, url = {https://ieeexplore.ieee.org/document/5755959}, year = 2008 }
  Link
  https://ieeexplore.ieee.org/document/5755959
3. V. R. Sidorenko, C. Senger, M. Bossert, and V. V. Zyablov, “Single-Trial Adaptive Decoding of Concatenated Codes,” in 11th International Workshop on Algebraic and Combinatorial Coding Theory (ACCT2008), Pamporovo, Bulgaria, 2008, pp. 260–266 [Online]. Available: http://www.moi.math.bas.bg/acct2008/b44.pdf
  - BibTeX
  - Link
  BibTeX
  @inproceedings{ref18, address = {Pamporovo, Bulgaria}, author = {Sidorenko, Vladimir R and Senger, Christian and Bossert, Martin and Zyablov, Victor V}, booktitle = {11th International Workshop on Algebraic and Combinatorial Coding Theory (ACCT2008)}, pages = {260 - 266}, title = {Single-Trial Adaptive Decoding of Concatenated Codes}, url = {http://www.moi.math.bas.bg/acct2008/b44.pdf}, year = 2008 }
  Link
  http://www.moi.math.bas.bg/acct2008/b44.pdf

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Christian Senger (IEEE S'05-M'11) is an Akademischer Oberrat at the Institute of Telecommunications at the University of Stuttgart. He received a diploma degree (M.Sc. equiv.) in Computer Science from Universität Karlsruhe (now Karlsruhe Institute of Technology) in 2006 and a Dr.-Ing. degree (Ph.D. equiv.) in Electrical Engineering from Ulm University in 2011. From May 2013 to October 2015, he was a postdoctoral research fellow at the Communications Group at the University of Toronto. His main field of interest is error control coding with its modern applications in fiber-optical high-speed networks, distributed data storage, and flash memories.

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