Successive Cancellation Ordered Search Decoding of Modified $\boldsymbol{G}_N$-Coset Codes

TL;DR

This paper introduces SCOS, a tree search decoding algorithm for $oldsymbol{G}_N$-coset codes that achieves near-ML performance with adaptive complexity, outperforming existing decoders and enabling strong error detection without outer codes.

Contribution

The paper proposes SCOS, a novel decoding algorithm for $oldsymbol{G}_N$-coset codes that combines ML performance with adaptive complexity and eliminates the need for outer codes.

Findings

SCOS achieves near-ML decoding performance within 0.25 dB of the RCU bound.

SCOS outperforms Reed--Muller codes under ML decoding by up to 0.5 dB.

Modified SCOS provides strong error detection and outperforms CRC-aided polar codes at high SNR.

Abstract

A tree search algorithm called successive cancellation ordered search (SCOS) is proposed for $\boldsymbol{G}_N$-coset codes that implements maximum-likelihood (ML) decoding with adaptive complexity for transmission over binary-input AWGN channels. Unlike bit-flip decoders, no outer code is needed to terminate decoding; therefore, SCOS also applies to $\boldsymbol{G}_N$-coset codes modified with dynamic frozen bits. The average complexity is close to that of successive cancellation (SC) decoding at practical frame error rates (FERs) for codes with wide ranges of rate and lengths up to $512$ bits, which perform within $0.25$ dB or less from the random coding union bound and outperform Reed--Muller codes under ML decoding by up to $0.5$ dB. Simulations illustrate simultaneous gains for SCOS over SC-Fano, SC stack (SCS) and SC list (SCL) decoding in FER and the average complexity at various SNR regimes. SCOS is further extended by forcing it to look for candidates satisfying a threshold, thereby outperforming basic SCOS under complexity constraints. The modified SCOS enables strong error-detection capability without the need for an outer code. In particular, the $(128, 64)$ polarization-adjusted convolutional code under modified SCOS provides gains in overall and undetected FER compared to CRC-aided polar codes under SCL/dynamic SC flip decoding at high SNR.