Lattice Quantization with Side Information: Codes, Asymptotics, and Applications in Sensor Networks

TL;DR

This paper develops asymptotically optimal lattice quantizers for Gaussian sources with side information at the decoder, with applications to sensor networks, achieving performance close to theoretical bounds in high-correlation scenarios.

Contribution

The paper introduces a structured class of quantizers that are asymptotically optimal for Gaussian sources with side information, especially under high correlation conditions.

Findings

Quantizers can approach Wyner's bound in high-correlation regimes.

Application to sensor networks demonstrates practical relevance.

Analysis impacts understanding of large-scale wireless network capacity.

Abstract

We consider the problem of rate/distortion with side information available only at the decoder. For the case of jointly-Gaussian source X and side information Y, and mean-squared error distortion, Wyner proved in 1976 that the rate/distortion function for this problem is identical to the conditional rate/distortion function R_{X|Y}, assuming the side information Y is available at the encoder. In this paper we construct a structured class of asymptotically optimal quantizers for this problem: under the assumption of high correlation between source X and side information Y, we show there exist quantizers within our class whose performance comes arbitrarily close to Wyner's bound. As an application illustrating the relevance of the high-correlation asymptotics, we also explore the use of these quantizers in the context of a problem of data compression for sensor networks, in a setup involving a large number of devices collecting highly correlated measurements within a confined area. An important feature of our formulation is that, although the per-node throughput of the network tends to zero as network size increases, so does the amount of information generated by each transmitter. This is a situation likely to be encountered often in practice, which allows us to cast under new--and more ``optimistic''--light some negative results on the transport capacity of large-scale wireless networks.