Trellis Structure of Block Codes

Abstract

Trellis diagrams have been traditionally exploited for decoding of convolutional codes [197]. Trellis design procedures for linear block codes have been under investigation since 1974 when Bahl, Cocke, Jelinek and Raviv introduced a method of representing the words in an arbitrary linear block code by the path labels in the trellis [5]. It has been found by Wolf J. [204] that an arbitrary linear (n, k,d min ) block code over GF(q), q ≥ 2, can be represented by its trellis diagram which contains N c = n + 1 columns (or depths) and N s ≤ q min {k,n-k} states. He found that such a trellis, also known as a syndrome or a Wolf’s trellis, could be constructed for the soft maximum likelihood trellis decoding (SMLTD) of a code. However, syndrome trellises have a non-regular structure (except for some particular codes, such as cyclic codes) that complicates their practical implementation.