Maximum likelihood soft decoding of binary codes by projecting on Abelian group codes

An approach to fast maximum likelihood decoding of some binary codes is presented. The binary codewords are regarded as images of some C/sub g/ group code, called the projected code, defined over an Abelian group A. The neighbourhood of z, z/spl isin/A/sup N/, the vector of symbol-by-symbol soft decoding, is examined to identify the most likely codeword of C/sub g/. A small list of candidate codewords is prepared by employing certain elimination rules. A substantial reduction of computational complexity is achieved by this method.