Low-complexity decoding with the minimal function-equivalent trellis

In this paper, we examine the relation between the trellis complexity and the decoding complexity. It can be shown that the complexity of soft-decision decoding for block codes when using a trellis is dominated by the total number of branches in the trellis. The number of branches at each stage of the trellis is determined by using the rank/length profile of the generator matrix or the parity-check matrix for the given code. The problem of minimizing the decoding complexity will also be investigated, aiming to get the minimal trellis in a more general sense for a class of codes, called function-equivalent codes.