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 P_{FD} (u) , the probability of error associated with the feedback decoding of the u 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 P_{FD} (u) as u tends to infinity, when the limit exists, is termed P_{FD} , the steady-state probability of error of feedback decoding. Sufficient conditions on decoders are given in order for P_{FD} to exist, and two classes of minimum-distance decoders exhibited that meet these sufficient conditions. P_{FD} is calculated for an example using the binary-symmetric channel and found to satisfy P_{FD} \le P_{DD} where P_{DD} is the probability of error associated with feedback-free decoding of the same code.