n-Channel Entropy-Constrained Multiple-Description Lattice Vector Quantization

TL;DR

This paper derives analytical formulas for multi-channel lattice vector quantizers optimized for minimal distortion under entropy and packet-loss constraints, demonstrating improved performance with three-channel systems over traditional two-channel setups.

Contribution

It extends the analysis of multiple-description lattice vector quantization to three channels and proposes a method to optimize the number of descriptions for minimal distortion.

Findings

Analytical expressions for central and side quantizers under high-resolution assumptions.

Optimal number of descriptions for given source and network conditions.

Three-channel MD-LVQ outperforms two-channel systems in simulations.

Abstract

In this paper we derive analytical expressions for the central and side quantizers which, under high-resolutions assumptions, minimize the expected distortion of a symmetric multiple-description lattice vector quantization (MD-LVQ) system subject to entropy constraints on the side descriptions for given packet-loss probabilities. We consider a special case of the general n-channel symmetric multiple-description problem where only a single parameter controls the redundancy tradeoffs between the central and the side distortions. Previous work on two-channel MD-LVQ showed that the distortions of the side quantizers can be expressed through the normalized second moment of a sphere. We show here that this is also the case for three-channel MD-LVQ. Furthermore, we conjecture that this is true for the general n-channel MD-LVQ. For given source, target rate and packet-loss probabilities we find the optimal number of descriptions and construct the MD-LVQ system that minimizes the expected distortion. We verify theoretical expressions by numerical simulations and show in a practical setup that significant performance improvements can be achieved over state-of-the-art two-channel MD-LVQ by using three-channel MD-LVQ.