Generating Series for Error Statistics of Block Codes on Channels with Memory

Cecilio Pimentel

doi:10.14209/jcis.1998.2

Abstract

We present an analytical method for evaluating the performance of non-interleaved forward error correcting codes on channels that exhibit statistical dependence in the occurrence of errors. We consider a model for such a channel based on the probabilistic function of a Markov chain, also known as finite state channel (FSC) model. The main idea is to apply combinatorial methods to derive simple expressions for the probability of the number of symbol errors produced by the channel in terms of a coefficient in a formal power series. These methods are used to derive expressions for the codeword error probability of various practical coding schemes, including nonbinary block codes and the concatenation of two block codes. The general expressions are specialized for a Gilbert-Elliott channel with known model parameters, and numerical results are derived.

Highlights

The design of reliable communication systems has been an active area of research in the past few years
The following expressions are valid for the matrices P and IT: channel was generalized by Elliott [2] in 1963, yielding the well known Gilbert-Elliott channel, by introducing a param eter g, which is the probability that the error bit is one when the chain is in a good state
We have addressed the problem of evaluating the codeword error probability of error control schemes on general finite state channel (FSC) models

Summary

Postal 7800 - Recife - PE - 50711-970

Abstract - We present an analytical method for evaluating the performance of non-interleaved forward error correcting codes on channels that exhibit statistical dependence in the occurrence of errors. The main idea is to apply combinatorial methods to derive simple ex pressions for the probability of the number of symbol errors produced by the channel in terms of a coefficient in a formal power series. These methods are used to derive expressions for the codeword error probability of various practical cod ing schemes, including nonbinary block codes and the con catenation of two block codes. The general expressions are specialized for a Gilbert-Elliott channel with known model parameters, and numerical results are derived. Keywords - Generating series, error correcting codes, Gilbert-Elliott channels, channels with memory, performance of coded systems

INTRODUCTION

EXAMPLE

PERFORMANCE ANALYSIS

CONCLUSIONS