Data Processing Bounds for Scalar Lossy Source Codes with Side Information at the Decoder

TL;DR

This paper develops new lower bounds on the distortion in scalar lossy source coding with decoder side information, using generalized data processing inequalities, and demonstrates their superiority over Wyner-Ziv bounds for certain sources.

Contribution

It introduces novel lower bounds on distortion by applying generalized data processing inequalities with alternative functions, extending previous bounds.

Findings

Bounds outperform Wyner-Ziv rate-distortion bounds for uniform sources.

Replacing the logarithm with other functions yields tighter bounds.

Results are applicable to convex functions like $Q(t)=t^{1-eta}$, $eta>1$.

Abstract

In this paper, we introduce new lower bounds on the distortion of scalar fixed-rate codes for lossy compression with side information available at the receiver. These bounds are derived by presenting the relevant random variables as a Markov chain and applying generalized data processing inequalities a la Ziv and Zakai. We show that by replacing the logarithmic function with other functions, in the data processing theorem we formulate, we obtain new lower bounds on the distortion of scalar coding with side information at the decoder. The usefulness of these results is demonstrated for uniform sources and the convex function $Q(t)=t^{1-\alpha}$, $\alpha>1$. The bounds in this case are shown to be better than one can obtain from the Wyner-Ziv rate-distortion function.