ML Soft-decision Decoding for Binary Linear Block Codes Based on Trellises of Their Supercodes

Based on the notion of supercodes, we propose a two-phase maximum-likelihood (ML) soft-decision decoding (tpMLSD) algorithm for binary linear block codes in this work. The first phase applies the priority-first search 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 to find the ML decision with a constant complexity per information bit at high signal-to-noise ratios (SNRs). Simulations on the extended BCH code of n = 64 and k = 24 show that the proposed two-phase scheme is an order of magnitude more efficient in average decoding complexity than the recursive ML decoding [1] when the SNR per information bit is 8 dB.