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 forPFD (u), the probability of error associated with the feedback decoding of theuth 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 ofPFD (u)asutends to infinity, when the limit exists, is termedPFD, the steady-state probability of error of feedback decoding. Sufficient conditions on decoders are given in order forPFDto exist, and two classes of minimum-distance decoders exhibited that meet these sufficient conditions.PFDis calculated for an example using the binary-symmetric channel and found to satisfyPFD ≤ PDDwherePDDis the probability of error associated with feedback-free decoding of the same code.