Efficient permutation criterion for obtaining minimal trellis of a block code

Abstract

To reduce the decoding complexity efficiently when using a trellis, a criterion is introduced, which can indicate at each stage of decoding whether or not the appropriate permutations on columns of the generator or parity-check matrix of the code are needed to obtain the minimal trellis in terms of its complexity. This criterion can also be used as a guide for finding a way to carry out column permutations more efficiently, as will be shown in an example.