Decoding of convolutional codes using a syndrome trellis

Soft-decision maximum-likelihood decoding of convolutional codes using the Viterbi algorithm with a syndrome trellis is proposed. The parity check matrix of a convolutional code is used to construct the trellis. This trellis is minimal. The number of operations for the decoding of one block of a q-ary rate k/n convolutional code is ~nq^min(k,n-k)q^ν, where ν is the memory size of the code. When the code rate satisfies k/n>½, the proposed algorithm is simpler than the classical Viterbi algorithm that has complexity ~nq^kq^ν