Error control coding: Algebraic and convolutional codes (ECC)
Lecture | ||||||||||
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Lecturer | Dr.-Ing. Christian Senger | |||||||||
Date | Mon 8:00 - 9:30 am and 2:00 to 3:30 pm | |||||||||
Lecture hall | Pfaff. 47, V 47.04 (PF47/U1/V 47.04) | |||||||||
Extent | 4 credit hours, 6 credit points | |||||||||
Language | English | |||||||||
Learning outcome | At the end of the course, students should have a good understanding of the most important algebraic and convolutional codes on a level that is sufficient to understand research papers in the area. Students should be able to choose appropriate code constructions and parameters when provided with the constraints of a communication system. They should also be able to implement efficient encoders and decoders. | |||||||||
Content |
Transmission errors are inherent to digital communication systems both in space (from here to there) and time (from now to later). A transmitted "1" might be detected as a "0" by the receiver and vice versa due to various channel impairments. A naive approach for correcting such errors is to transmit every bit, say, n > 1 times and then take a majority decision at the receiver. This simple example already explains the basic concept behind error control coding: a block of information (here a single bit) is augmented by redundancy (here n-1 bits) in order to correct a certain number of transmission errors (here no more than (n-1)/2 bits). In other words, transmission rate is traded in for error resilience. |
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Literature | Roth: Introduction to Coding Theory (Cambridge University Press) | |||||||||
Figure Example |
Visualizing decoding of Reed-Solomon codes using polynomials |
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Material | ILIAS |
Module description in LSF