Convolutional codes II. Maximum-likelihood decoding

Convolutional codes are characterized by a trellis structure. Maximum-likelihood decoding is characterized as the finding of the shortest path through the code trellis, an efficient solution for which is the Viterbi algorithm. A universal asymptotic bounding technique is developed and used to bound error probability, free distance, list-of-2 error probability, and other subsidiary quantities. The bounds are dominated by what happens at a certain critical length Nerit. Termination of a convolutional code to length Nerit or shorter results in an optimum block code. In general, block code exponents can be related to convolutional code exponents and vice versa by a graphical construction, called the concatenation construction. It is shown that termination is unnecessary with the Viterbi algorithm