n-Channel Asymmetric Multiple-Description Lattice Vector Quantization

TL;DR

This paper derives optimal entropy-constrained lattice vector quantizers for asymmetric multiple-description coding, minimizing expected distortion under packet-loss probabilities, with analytical expressions valid for any number of descriptions and dimensions.

Contribution

It provides analytical formulas for optimal asymmetric multiple-description lattice vector quantizers, including optimal bit distribution and second moments, applicable to any number of descriptions and dimensions.

Findings

Normalized second moments match those of an L-dimensional sphere.

Optimal bit distribution among descriptions is not unique.

Derived expressions are valid under high-resolution assumptions.

Abstract

We present analytical expressions for optimal entropy-constrained multiple-description lattice vector quantizers which, under high-resolutions assumptions, minimize the expected distortion for given packet-loss probabilities. We consider the asymmetric case where packet-loss probabilities and side entropies are allowed to be unequal and find optimal quantizers for any number of descriptions in any dimension. We show that the normalized second moments of the side-quantizers are given by that of an $L$-dimensional sphere independent of the choice of lattices. Furthermore, we show that the optimal bit-distribution among the descriptions is not unique. In fact, within certain limits, bits can be arbitrarily distributed.