Large deviations on empirical service for erasure channels with memory

This article examines the performance of a digital communication link from a large deviations perspective. The underlying physical environment is modeled as an erasure channel with memory. Information is shielded from symbol erasures using error-correcting codes with finite block-lengths. At the onset of the communication process, the transmit buffer is assumed to contain a certain number of data bits; these bits are partitioned into segments and subsequently transmitted as coded packets. Acknowledgments of successful transmissions are obtained through periodic, reliable feedback. Performance criteria are derived based on the average service rate and the first-passage time to an empty queue. The optimization problem is posed in an asymptotic setting and large deviation principles are obtained for these two quantities. The proposed analysis framework provides a methodology tailored to code rate and block-length selection for delay-sensitive applications. This study leads to pertinent guidelines on how to choose system parameters for communication over correlated channels. Examples obtained through a numerical study are included to further illustrate the value of the techniques introduced in this paper.