Efficient maximum likelihood decoding of linear block codes using a trellis

It is shown that soft decision maximum likelihood decoding of any (n,k) linear block code over GF(q) can be accomplished using the Viterbi algorithm applied to a trellis with no more than q (n-k) states. For cyclic codes, the trellis is periodic. When this technique is applied to the decoding of product codes, the number of states in the trellis can be much fewer than q n-k. For a binary (n,rz 1) single parity check code, the Viterbi algorithm is equivalent to the Wagner decoding algorithm.