Trellis representation of codes
Kluwer Academic Publishers eBooks · 2006
In Chapter 3 we described a technique to introduce an algebraic structure into a signal constellation S obtained as a subset of X n . X = {±1} . This technique generates linear binary codes. Each of these cedes can be represented in two ways: either as the set of all linear combinations of the rows of a generator matrix or as the set of all binary n-tuples that satisfy some parity-check equations. The present chapter describes an exceedingly convenient representation of linear block codes as the set of all n-tuples corresponding to paths traversing a trellis . This representation can be used for optimal decoding based on the Viterbi algorithm. The complexity of this trellis representation is also examined. and minimal trellises are introduced. The complexity of trellis representations can be further reduced by introducing tail-biting trellises. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.