Generating series and performance bounds for convolutional codes over burst-error channels

Abstract

We present an analytical method for evaluating performance bounds for a communication system that employs a convolutional code, a block interleaving with finite interleaving depth, a binary channel that exhibits statistical dependence in the occurrence of errors, and a decoder that implements the Viterbi (1979) algorithm with Hamming metric. The main idea is to apply combinatorial methods to derive a formula for bounds to first-event and bit error probabilities in terms of coefficients of a generating series. The method is used to investigate the tradeoff between coding parameters and interleaving depth to achieve a required performance.