Analysis of decoders for convolutional codes by stochastic sequential machine methods

Abstract
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 forP_{FD} (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 ofP_{FD} (u)asutends to infinity, when the limit exists, is termedP_{FD}, the steady-state probability of error of feedback decoding. Sufficient conditions on decoders are given in order forP_{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 satisfyP_{FD} \le P_{DD}whereP_{DD}is the probability of error associated with feedback-free decoding of the same code.

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