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Title: Successive-Cancellation Decoding of Reed-Muller Codes with Fast Hadamard Transform

Abstract: In this paper we propose efficient decoding techniques to significantly improve the error-correction performance of fast successive-cancellation (FSC) and FSC list (FSCL) decoding algorithms for short low-order Reed-Muller (RM) codes. In particular, we first integrate Fast Hadamard Transform (FHT) into FSC (FHT-FSC) and FSCL (FHT-FSCL) decoding algorithms to optimally decode the first-order RM subcodes. We then utilize the rich permutation group of RM codes by independently running the FHT-FSC and the FHT-FSCL decoders on a list of random bit-index permutations of the codes. The simulation results show that the error-correction performance of the FHT-FSC decoders on a list of $L$ random code permutations outperforms that of the FSCL decoder with list size $L$, while requiring lower memory requirement and computational complexity for various configurations of the RM codes. In addition, when compared with the state-of-the-art recursive projection-aggregation (RPA) decoding, the permuted FHT-FSCL decoder can obtain a similar error probability for the RM codes of lengths $128$, $256$, and $512$ at various code rates, while requiring several orders of magnitude lower computational complexity.
 Comments: Submitted to an IEEE journal for possible publication Subjects: Information Theory (cs.IT) Cite as: arXiv:2108.12550 [cs.IT] (or arXiv:2108.12550v2 [cs.IT] for this version)

Submission history

From: Nghia Doan Mr. [view email]
[v1] Sat, 28 Aug 2021 02:11:21 GMT (51kb)
[v2] Tue, 31 Aug 2021 21:23:20 GMT (52kb)

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