On viterbi-like algorithms and their application to Reed–Muller codes

Abstract

For a Viterbi-like algorithm over a sectionalized trellis of a linear block code, the decoding procedure consists of three parts: computingthe metrics of the edges, selectingthe survivor edge between each pair of adjacent vertices and determining the survivor path from the origin to each vertex. In this paper, some new methods for computingthe metrics of the edges are proposed. Our method of ‘‘partition of index set’’ for computing the metrics is shown to be near-optimal. The proposed methods are then applied to Reed–Muller (RM) codes. For some RM codes, the computational complexity of decodingis significantly reduced in comparison to the best-known ones. For the RM codes, a direct method for constructingtheir trellis-oriented-generator-matrices is proposed and some shift invariances are deduced.