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

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