Low-complexity decoding of partial unit memory codes on precoded partial-response channels

Cosets of convolutional codes can be used to obtain large free Euclidean distances and short maximum zero-run lengths at the output of the 1-D partial-response channel (PRC). We present a new soft-decision decoding technique for cosets of convolutional codes on the preceded 1-D PRC. The decoding technique is especially well suited for cosets of partial unit memory (PUM) convolutional codes. A connection between the decoder trellises for cosets of block codes and PUM codes on the 1-D PRC is exploited to obtain a small number of operations per decoded information bit. We prove that the new decoding technique needs fewer operations than the Viterbi algorithm for any (n,n-r), r⩾1, PUM code coset with n⩽2^v-r where v is the constraint length. It is also indicated how to prove the same result for other classes of codes. For many of the best known PUM code cosets, the new decoding technique requires both fewer operations per decoded information bit and smaller path memories than the Viterbi algorithm needs for comparable cosets of punctured convolutional codes