Sequential Coding of Markov Sources over Burst Erasure Channels

TL;DR

This paper investigates the minimum rate for sequentially compressing Markov sources over burst erasure channels, providing bounds, optimal schemes, and scaling behaviors for various source classes and constraints.

Contribution

It introduces the rate-recovery function for Markov sources over burst erasure channels, derives bounds, and proposes optimal coding schemes including prospicient coding for semi-deterministic sources.

Findings

Upper and lower bounds on the rate-recovery function coincide in some cases.

The rate scales as predictive coding rate plus a decreasing term with W.

Prospicient coding is optimal for semi-deterministic Markov sources.

Abstract

We study sequential coding of Markov sources under an error propagation constraint. An encoder sequentially compresses a sequence of vector-sources that are spatially i.i.d. but temporally correlated according to a first-order Markov process. The channel erases up to B packets in a single burst, but reveals all other packets to the destination. The destination is required to reproduce all the source-vectors instantaneously and in a lossless manner, except those sequences that occur in an error propagation window of length B + W following the start of the erasure burst. We define the rate-recovery function R(B, W) - the minimum achievable compression rate per source sample in this framework - and develop upper and lower bounds on this function. Our upper bound is obtained using a random binning technique, whereas our lower bound is obtained by drawing connections to multi-terminal source coding. Our upper and lower bounds coincide, yielding R(B, W), in some special cases. More generally, both the upper and lower bounds equal the rate for predictive coding plus a term that decreases as 1/(W+1), thus establishing a scaling behaviour of the rate-recovery function. For a special class of semi-deterministic Markov sources we propose a new optimal coding scheme: prospicient coding. An extension of this coding technique to Gaussian sources is also developed. For the class of symmetric Markov sources and memoryless encoders, we establish the optimality of random binning. When the destination is required to reproduce each source sequence with a fixed delay and when W = 0 we also establish the optimality of binning.