Nested Lattice Codes for Arbitrary Continuous Sources and Channels

TL;DR

This paper demonstrates that nested lattice codes are capable of achieving capacity and optimal source coding for arbitrary continuous sources and channels, regardless of the presence of side information.

Contribution

It establishes the optimality of nested lattice codes for both channel capacity and source coding in a broad, continuous setting with or without side information.

Findings

Nested lattice codes achieve channel capacity for arbitrary channels.

Nested lattice codes are optimal for source coding with side information.

The results hold for both causal and non-causal side information.

Abstract

In this paper, we show that nested lattice codes achieve the capacity of arbitrary channels with or without non-casual state information at the transmitter. We also show that nested lattice codes are optimal for source coding with or without non-causal side information at the receiver for arbitrary continuous sources.