Analysis of burst errors in communication networks and their control with applications to ISDN

Abstract

The main objective of this dissertation is to investigate how well the channel memory (statistical dependence in the occurrence of transmission errors) can be used in the evaluation and the design of error control schemes an a unified framework. It is well known that error distributions encountered on operational digital communications systems are generally bursty in nature. Errors introduced on most channels are not independent and cannot be adequately represented by the classical memoryless binary symmetric channel model. Further, error processes on real channels differ from one another in varying degrees of burstiness. Thus, in selecting the most suitable error control technique to combat channel errors, the statistical properties of the channel error process which adequately describe the channel behavior should fully be used. For this purpose, in this dissertation we first developed a bit-level Markovian error model, and obtained recurrence relations for the dependency of P(m, n) on n. We solved this set of recursive relations by using the z-transform approach. Then computed several moments of P(m, n). Further, by aggregating the bit-level model, we developed a block-level model and derived the joint probability distribution of errors between two adjacent blocks of equal sizes. The block-level model was extended to a two-state Markov chain describing the error correlation structure between blocks, in which each block is divided into two states according to whether more than a specified number of bits are in error. Particularly, we concentrated on a special case named as the simplest Markovian block error pattern with two states, in which each block is classified into two classes of whether the block transmission is in error or not. We presented numerical and simulation results for the simplest Markovian block error pattern and compared them to those for the conventional memoryless channel, in order to understand the relationships between several param...