Zero-Delay Sequential Transmission of Markov Sources Over Burst Erasure Channels

TL;DR

This paper investigates the minimum compression rate needed for zero-delay sequential transmission of Markov sources over burst erasure channels, providing bounds and exact characterizations for different source types and recovery scenarios.

Contribution

It introduces bounds and exact solutions for the rate-recovery function in zero-delay transmission of Markov sources over burst erasure channels, extending understanding of optimal coding strategies.

Findings

Bounds on the rate-recovery function for discrete sources are established.

Bounds coincide in the high resolution limit for Gauss-Markov sources.

The rate-recovery function is fully characterized for i.i.d. Gaussian sources.

Abstract

A setup involving zero-delay sequential transmission of a vector Markov source over a burst erasure channel is studied. A sequence of source vectors is compressed in a causal fashion at the encoder, and the resulting output is transmitted over a burst erasure channel. The destination is required to reconstruct each source vector with zero-delay, but those source sequences that are observed either during the burst erasure, or in the interval of length $W$ following the burst erasure need not be reconstructed. The minimum achievable compression rate is called the rate-recovery function. We assume that each source vector is sampled i.i.d. across the spatial dimension and from a stationary, first-order Markov process across the temporal dimension. For discrete sources the case of lossless recovery is considered, and upper and lower bounds on the rate-recovery function are established. Both these bounds can be expressed as the rate for predictive coding, plus a term that decreases at least inversely with the recovery window length $W$. For Gauss-Markov sources and a quadratic distortion measure, upper and lower bounds on the minimum rate are established when $W=0$. These bounds are shown to coincide in the high resolution limit. Finally another setup involving i.i.d. Gaussian sources is studied and the rate-recovery function is completely characterized in this case.