Complexity-Adaptive Maximum-Likelihood Decoding of Modified $\boldsymbol{G}_N$-Coset Codes

TL;DR

This paper introduces a complexity-adaptive ML decoding algorithm for G_N-coset codes, achieving near-ML performance with manageable complexity for polar and Reed-Muller codes, and applicable to dynamic frozen bits without extra termination codes.

Contribution

It presents a novel complexity-adaptive tree search algorithm for G_N-coset codes that balances near-ML decoding performance with practical complexity, applicable to various code modifications.

Findings

Average complexity close to successive cancellation decoding for short codes

Near-ML decoding for longer Reed-Muller codes and subcodes

No outer code needed for termination, suitable for dynamic frozen bits

Abstract

A complexity-adaptive tree search algorithm is proposed for $\boldsymbol{G}_N$-coset codes that implements maximum-likelihood (ML) decoding by using a successive decoding schedule. The average complexity is close to that of the successive cancellation (SC) decoding for practical error rates when applied to polar codes and short Reed-Muller (RM) codes, e.g., block lengths up to $N=128$. By modifying the algorithm to limit the worst-case complexity, one obtains a near-ML decoder for longer RM codes and their subcodes. Unlike other bit-flip decoders, no outer code is needed to terminate decoding. The algorithm can thus be applied to modified $\boldsymbol{G}_N$-coset code constructions with dynamic frozen bits. One advantage over sequential decoders is that there is no need to optimize a separate parameter.