Error exponents and test channel optimization for the Gaussian Wyner-Ziv problem

Abstract

We consider the quadratic Gaussian Wyner-Ziv problem, i.e., the problem of lossy compression of a Gaussian source with Gaussian side information at the decoder and a quadratic distortion measure. Motivated by applications in video coding, we study how to minimize the probability that the distortion exceeds a given threshold, as opposed to the conventional approach of minimizing the average distortion. We obtain an achievable exponent for this problem, which is positive above the rate distortion function, and expose a tension in the choice of the test channel; the optimal test channel balances two competing error events.

On the excess distortion exponent of the quadratic-Gaussian Wyner-Ziv problem

“…Indeed, this effect seems to be fundamental, and not tied to the lattice approach. A similar effect where distortion may be too high even when there is no binning error, is reported in [4] as well. In this work we show, that this loss vanishes in the limit of high rate.…”

“…However, the excess distortion exponent for this problem is as yet unknown, and in particular it is not clear whether there is a loss with respect to the excessdistortion exponent of the unknown part of the source. Recently, Kelly et al [4] derived an achievable exponent for the problem, which indeed reflects a loss.…”

Joint source-channel with side information coding error exponents

“…A game theoretic approach is applied to show the equivalence of the lower and upper bound. This approach might be useful in simplifying other error exponents with a cascade of min-max operators , for example, the Wyner-Ziv coding error exponent recently studied in [10]. …”

“…The goal of this paper is to derive a similar result for E(P AB , W Y |X ) defined in (2) as that for the joint source channel coding in ( 9) and (10).…”

“…the complete characterization as that in (10). It is simpler for the case in (9) since all is needed is that the sphere backing bound and the random coding bound to match at the critical rate R * as discussed in Section II-B.3.…”