First-Passage Time and Large-Deviation Analysis for Erasure Channels with Memory

TL;DR

This paper develops a rigorous framework for analyzing delay and large deviation performance in finite-state erasure channels with memory, aiding optimal code design for delay-sensitive communication systems.

Contribution

It introduces a methodology to compute buffer emptying time distribution and large deviation principles for service times in channels with memory, guiding code rate and block length selection.

Findings

Explicit delay-violation probabilities derived

Large deviation principles established for service times

Methodology applicable to practical communication systems

Abstract

This article considers the performance of digital communication systems transmitting messages over finite-state erasure channels with memory. Information bits are protected from channel erasures using error-correcting codes; successful receptions of codewords are acknowledged at the source through instantaneous feedback. The primary focus of this research is on delay-sensitive applications, codes with finite block lengths and, necessarily, non-vanishing probabilities of decoding failure. The contribution of this article is twofold. A methodology to compute the distribution of the time required to empty a buffer is introduced. Based on this distribution, the mean hitting time to an empty queue and delay-violation probabilities for specific thresholds can be computed explicitly. The proposed techniques apply to situations where the transmit buffer contains a predetermined number of information bits at the onset of the data transfer. Furthermore, as additional performance criteria, large deviation principles are obtained for the empirical mean service time and the average packet-transmission time associated with the communication process. This rigorous framework yields a pragmatic methodology to select code rate and block length for the communication unit as functions of the service requirements. Examples motivated by practical systems are provided to further illustrate the applicability of these techniques.