Efficient maximum likelihood decoding of linear block codes using a trellis

@article{Wolf1978EfficientML,
  title={Efficient maximum likelihood decoding of linear block codes using a trellis},
  author={Jack K. Wolf},
  journal={IEEE Trans. Information Theory},
  year={1978},
  volume={24},
  pages={76-80}
}
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. 
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