Expansion Coding for Channel and Source Coding

TL;DR

This paper introduces expansion coding, a method that simplifies analog channel and source coding problems by mapping them to discrete problems, achieving near-optimal performance with low-complexity codes.

Contribution

The paper proposes a novel expansion coding framework that reduces complex analog coding problems to simpler discrete problems, enabling efficient and near-optimal solutions.

Findings

Achieves capacity of AEN channel in high SNR regime.

Approaches Shannon limit for lossy compression at low distortion.

Enables low-complexity coding using discrete codes like polar codes.

Abstract

A general method of coding over expansion is proposed,which allows one to reduce the highly non-trivial problems of coding over analog channels and compressing analog sources to a set of much simpler subproblems, coding over discrete channels and compressing discrete sources. More specifically, the focus of this paper is on the additive exponential noise (AEN) channel, and lossy compression of exponential sources. Taking advantage of the essential decomposable property of these channels (sources), the proposed expansion method allows for mapping of these problems to coding over parallel channels (respectively, sources), where each level is modeled as an independent coding problem over discrete alphabets. Any feasible solution to the resulting optimization problem after expansion corresponds to an achievable scheme of the original problem. Utilizing this mapping, even for the cases where the optimal solutions are difficult to characterize, it is shown that the expansion coding scheme still performs well with appropriate choices of parameters. More specifically, theoretical analysis and numerical results reveal that expansion coding achieves the capacity of AEN channel in the high SNR regime. It is also shown that for lossy compression, the achievable rate distortion pair by expansion coding approaches to the Shannon limit in the low distortion region. Remarkably, by using capacity-achieving codes with low encoding and decoding complexity that are originally designed for discrete alphabets, for instance polar codes, the proposed expansion coding scheme allows for designing low-complexity analog channel and source codes.