Lattices from Linear Codes: Source and Channel Networks

TL;DR

This paper develops a framework for analyzing achievable rates and distortions in complex multiterminal communication systems with continuous sources and channels, using discretization and lattice-like codes.

Contribution

It introduces a discretization-based framework for characterizing limits and constructs lattice-like codes for various sources and channels, advancing multiterminal information theory.

Findings

Convergence results for information measures under discretization

Inner-bounds for achievable rates and distortions

Construction of lattice-like codes for general sources and channels

Abstract

In this paper, we consider the information-theoretic characterization of the set of achievable rates and distortions in a broad class of multiterminal communication scenarios with general continuous-valued sources and channels. A framework is presented which involves fine discretization of the source and channel variables followed by communication over the resulting discretized network. In order to evaluate fundamental performance limits, convergence results for information measures are provided under the proposed discretization process. Using this framework, we consider point-to-point source coding and channel coding with side-information, distributed source coding with distortion constraints, the function reconstruction problems (two-help-one), computation over multiple access channel, the interference channel, and the multiple-descriptions source coding problem. We construct lattice-like codes for general sources and channels, and derive inner-bounds to set of achievable rates and distortions in these communication scenarios.