Maximum-likelihood Soft-decision Decoding for Binary Linear Block Codes Based on Their Supercodes

TL;DR

This paper introduces a two-phase maximum-likelihood soft-decision decoding algorithm for binary linear block codes using supercodes, significantly improving decoding efficiency over traditional methods at certain SNR levels.

Contribution

The paper presents a novel two-phase decoding scheme leveraging supercodes and combines Viterbi and priority-first search algorithms for improved efficiency.

Findings

Decoding complexity is reduced by an order of magnitude at 4.5 dB SNR.

The method guarantees maximum-likelihood decision accuracy.

Simulations on Reed-Muller codes validate the efficiency gains.

Abstract

Based on the notion of supercodes, we propose a two-phase maximum-likelihood soft-decision decoding (tpMLSD) algorithm for binary linear block codes in this work. The first phase applies the Viterbi algorithm backwardly to a trellis derived from the parity-check matrix of the supercode of the linear block code. Using the information retained from the first phase, the second phase employs the priority-first search algorithm to the trellis corresponding to the linear block code itself, which guarantees finding the ML decision. Simulations on Reed-Muller codes show that the proposed two-phase scheme is an order of magnitude more efficient in average decoding complexity than the recursive maximum-likelihood decoding (RMLD) [1] when the signal-to-noise ratio per information bit is 4.5 dB.