Probabilistic construction of trellis codes

A new approach to constructing good long trellis codes for use with Sequential Decoding (SD) is proposed. The procedure begins by choosing a relatively small set of codes randomly. The error performance of each of these codes is evaluated using sequential decoding and the code with the best performance among the chosen set is retained. The performance of many of the randomly chosen codes is quite good. This is consistent with the well known fact that a randomly chosen code is very likely to be a good code. It is surprising to find out that the new codes found using this approach, which come from a very small set of codes compared to the total number of possible codes, perform about as well as the best known codes. The best short codes can be found by exhaustive search. This is the approach used to construct codes for Viterbi decoding, whose complexity prohibits the use of long codes. On the other hand, the complexity of SD is essentially independent of the code constraint length. The approach proposed here thus provides an excellent way of constructing long codes for use with SD, since an exhaustive search for the best long codes is impractical.