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 parameters of the derived models.
Next, we showed that the block-level model obtained is very comprehensive and can be used for derivation of a number of parameters in evaluating the performance of a block-oriented data communication system. In this way, we first proposed and evaluated two modified ARQ schemes in which the error patterns for both forward and backward channels are given by the derived simplest Markovian block error pattern. One is referred to as the modified go-back-N ARQ scheme with timer control in which recovery actions of erroneous block transmission are initiated with the expiration of timer. The other is referred to as the modified go-back-N ARQ scheme with buffer control in which erroneous blocks are retransmitted when the retransmission buffer becomes full. We first described protocol descriptions of the two schemes, and performed an exact analysis of their throughput and delay behaviors by using the signal flow graph method, and quantified how much the performance is affected by the degree of error burstiness in backward (acknowledgment) channel. Also, we showed the effects of timer value and buffer size on the performance.
In addition, we applied the derived simplest Markovian block error pattern to the performance evaluation of the practical link-level procedures, LAPB/D with multireject options, and investigated both throughput and user-perceived response time behaviors to determine how much the performance of error recovery action is improved under this burst error condition. The performance was first evaluated in a continuous-time domain. Next, to eliminate the computational complexity in the continuous-time domain, we presented an approximate discrete-time analysis. Through numerical examples, we showed that the simplest Markovian block error pattern is superior in throughput and delay characteristics to the random(independent) error case. In this study, instead of mean alone, we used a new measure of the response time specified as mean plus two standard deviations so as to consider the user-perceived worst cases, and also showed that it results in much greater sensitivity to parameter variations than does mean value alone, and in this respect is a useful measure of response time for representing the user-perceived response time.
Finally, we applied the derived block-level model to the evaluation of a digital tandem connection consisting of a set of segment channels. Then, using the stochastic sequential machine technique we evaluated the performance of end-to-end error control by deriving several end-to-end error statistics of the tandem connection, including covariance and autocorrelation functions, block error gap distribution, average block error rate, and so forth. We also described a method of state aggregation that approximates the tandem model parameters by combining individual segment channels into an equivalent tandem connection. We showed that a description of the error performance of such tandem connection (equivalent to a hypothetical reference connection) is very useful for allocating network performance objectives among segment channels (corresponding to the circuits composing of a hypothetical reference connection). We also showed there exists a large difference between the performances with the burst error structure and with a conventional independent-error approach.
