Analysis of decoders for convolutional codes by stochastic sequential machine methods

In this paper, the decoder of a convolutional code is modeled as an autonomous stochastic sequential machine and finite Markov chain theory applied to obtain a precise expression for , the probability of error associated with the feedback decoding of the th subblock of information digits. The analysis technique developed extends directly to any convolutional decoder for a linear convolutional code, used for transmission over a finite state channel. The limit of as tends to infinity, when the limit exists, is termed , the steady-state probability of error of feedback decoding. Sufficient conditions on decoders are given in order for to exist, and two classes of minimum-distance decoders exhibited that meet these sufficient conditions. is calculated for an example using the binary-symmetric channel and found to satisfy where is the probability of error associated with feedback-free decoding of the same code.