Soft-Output Successive Cancellation List Decoding

TL;DR

This paper presents a novel soft-output successive cancellation list decoding algorithm that improves error performance and reliability in decoding dynamic Reed-Muller, polar, and LDPC codes, with practical constraints on misdetection rates.

Contribution

It introduces an approximation method compatible with all SC-based decoders and develops soft-output SCL decoding, enhancing decoding accuracy and practical applicability.

Findings

SO-SCL outperforms CRC-polar codes in BLER and UER

Decoding Misdetection Rate (MDR) can be constrained to predefined levels

Simulation shows significant improvements over existing list-max and list-sum methods

Abstract

We introduce an algorithm for approximating the codebook probability that is compatible with all successive cancellation (SC)-based decoding algorithms, including SC list (SCL) decoding. This approximation is based on an auxiliary distribution that mimics the dynamics of decoding algorithms with an SC decoding schedule. Based on this codebook probability and SCL decoding, we introduce soft-output SCL (SO-SCL) to generate both blockwise and bitwise soft-output (SO). Using that blockwise SO, we first establish that, in terms of both block error rate (BLER) and undetected error rate (UER), SO-SCL decoding of dynamic Reed-Muller (RM) codes significantly outperforms the CRC-concatenated polar codes from 5G New Radio under SCL decoding. Moreover, using SO-SCL, the decoding misdetection rate (MDR) can be constrained to not exceed any predefined value, making it suitable for practical systems. Proposed bitwise SO can be readily generated from blockwise SO via a weighted sum of beliefs that includes a term where SO is weighted by the codebook probability, resulting in a soft-input soft-output (SISO) decoder. Simulation results for SO-SCL iterative decoding of product codes and generalized LDPC (GLDPC) codes, along with information-theoretical analysis, demonstrate significant superiority over existing list-max and list-sum approximations.