Queueing behavior of the Gilbert-Elliott channel: BCH codes and Poisson arrivals

This paper considers the queueing performance of a communication system that transmits BCH-coded data over the correlated-error channel first studied by Gilbert and Elliott in the 1960s. For some arrival processes, one can join the queue length and channel state so that the pair forms a Markov chain; this provides a powerful tool to analyze the tail probability of the queue. For Bernoulli packet arrivals, this approach works but does not allow for fair comparisons between different block-length codes. In this paper, a Poisson arrival model is assumed in order to make fair comparisons between codes with arbitrary block length and code rate. This enables one to optimize code parameters for delay-sensitive communication systems over time-varying channels. Finally, the analysis is supported through a Monte Carlo simulation.