On Error Exponents and Moderate Deviations for Lossless Streaming Compression of Correlated Sources

TL;DR

This paper establishes bounds on error exponents and moderate deviations for lossless streaming compression of correlated sources, revealing conditions under which these bounds coincide and providing a comprehensive characterization of the error behavior.

Contribution

It derives the first bounds on error exponents and moderate deviations for correlated source compression in streaming settings, including conditions for their tightness.

Findings

Bounds for error exponents are tight under certain rate conditions.

Moderate deviations constants are characterized for both blockwise and symbolwise codes.

An information spectrum-type strong converse is established for blockwise codes.

Abstract

We derive upper and lower bounds for the error exponents of lossless streaming compression of two correlated sources under the blockwise and symbolwise settings. We consider the linear scaling regime in which the delay is a scalar multiple of the number of symbol pairs of interest. We show that for rate pairs satisfying certain constraints, the upper and lower bounds for the error exponent of blockwise codes coincide. For symbolwise codes, the bounds coincide for rate pairs satisfying the aforementioned constraints and a certain condition on the symbol pairs we wish to decode---namely, that their indices are asymptotically comparable to the blocklength. We also derive moderate deviations constants for blockwise and symbolwise codes, leveraging the error exponent results, and using appropriate Taylor series expansions. In particular, for blockwise codes, we derive an information spectrum-type strong converse, giving the complete characterization of the moderate deviations constants. For symbolwise codes, under an additional requirement on the backoff from the first-order fundamental limit, we can show that the moderate deviations constants are the same as the blockwise setting.