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/spl ges/1, PUM code coset with n/spl les/2/sup 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.

Consider a cycle in the state diagram of a convolutional code. The average weight per branch of the cycle is equal to the total Hamming weight of all labels on the branches divided by the number of branches. Let w/sub 0/ be the minimum average weight per branch over all cycles in the state diagram, except the zero state self-loop of weight zero. Codes with low w/sub 0/ result in high bit error probabilities when they are used with either Viterbi or sequential decoding. Hemmati and Costello (1980) showed that w/sub 0/ is upper-bounded by 2/sup /spl nu/-2//(3/spl middot/2/sup /spl nu/-2/-1) for a class of (2,1) codes where /spl nu/ denotes the constraint length. In the present correspondence it is shown that the bound is valid for a large class of (n,n-1) codes, n/spl ges/2. Examples of high-rate codes with w/sub 0/ equal to the upper bound are also given. Hemmati and Costello defined a class of codes to be asymptotically catastrophic if w/sub 0/ approaches zero for large /spl nu/. The class of (n,n-1) codes constructed by Wyner and Ash (1963) is shown to be asymptotically catastrophic. All codes in the class have minimum possible w/sub 0/ equal to 1//spl nu/.

We present a new soft-decision decoding method for high-rate convolutional codes. The decoding method is especially well-suited for PUM convolutional codes. The method exploits the linearity of the parallel transitions in the trellis associated with PUM codes. We provide bounds on the number of operations per decoded bit, and show that this number is dependent on the weight hierarchy of the linear block code associated with the parallel transitions. The complexity of the new decoding method for PUM codes is compared to the complexity of Viterbi decoding of comparable punctured convolutional codes. Examples from a special class of PUM codes show that the new decoding method compares favorably to Viterbi decoding of punctured codes.