On Optimum Decoding of Certain Product Codes

Optimum decoding of a class of product codes is investigated. The class is the one given by the serial concatenation of a binary single-parity-check code with a low-dimension binary linear block code. It was proved by Wolf that maximum likelihood decoding for this class of product codes can be efficiently performed through the Viterbi algorithm over a compact trellis representation of the code. In this letter, it is showed that the decoding complexity can be further reduced by formulating the decoding problem as a symbol-wise maximum-a-posteriori decision problem. Results illustrated for suitably designed codes show that the proposed algorithm significantly outperforms conventional iterative decoders. Finally, a generalization of the code construction, enjoying the same low-complexity decoding principle is presented and analyzed, achieving tangible coding gains at moderate error rates.