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Recursive list decoding for Reed-Muller codes and their subcodes. (English) Zbl 1071.94025
Blaum, Mario (ed.) et al., Information, coding and mathematics. Proceedings of workshop honoring Professor Bob McEliece on his 60th birthday, Pasadena, CA, USA, May 24–25, 2002. Boston, MA: Kluwer Academic Publishers (ISBN 1-4020-7079-9/hbk). The Kluwer International Series in Engineering and Computer Science 687, 279-298 (2002).
This paper considers recursive structure of Reed-Muller (RM) codes in detail. Decoding techniques have been considered and two different versions of their recursive algorithm have been designed. Decoding performance has been shown to improve considerably by using subcodes of RM codes. Another improvement is based on using relatively short lists of codewords in the intermediate steps of recursion. The authors use different permutations taken from the symmetry (automorphism) group of the code. For moderate lengths upto 512, near-optimum decoding with feasible complexity has been obtained.
For the entire collection see [Zbl 1054.94001].
94B15 Cyclic codes
94B35 Decoding