First-passage time analysis for digital communication over erasure channels with delay-sensitive traffic

This article explores the relation between queueing behavior and code-rate selection for digital communication over correlated erasure channels. The focus is on non-asymptotic system analysis, with finite block-lengths and non-vanishing probabilities of decoding failure. The transmit buffer is assumed to possess a given initial distribution and performance is evaluated in terms of the time required for the queue to become empty. Special attention is given to channel memory and its impact on the decoding process at the receiver. The system is ultimately defined in terms of a finite-state erasure channel. Using a Markov structure, the evolution of the transmit buffer is characterized and the distribution of the first-passage time to an empty queue is obtained. The proposed methodology is employed to optimally select code-rate. This provides new insights on the natural tradeoff between error protection and data content in the finite block-length regime.