On viterbi-like algorithms and their application to Reed–Muller codes
Date of Issue2004
School of Physical and Mathematical Sciences
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.
Journal of complexity
© 2004 Elsevier Inc. This is the author created version of a work that has been peer reviewed and accepted for publication by Journal of Complexity, Elsevier Inc. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1016/j.jco.2004.01.003].