Lossy Compression of Exponential and Laplacian Sources using Expansion Coding

TL;DR

This paper introduces an expansion coding method for lossy compression of exponential and Laplacian sources, transforming the problem into simpler discrete source coding tasks, especially effective at low distortions with manageable complexity.

Contribution

The paper proposes a novel expansion coding scheme that reduces continuous source compression to parallel discrete problems, enabling practical low-complexity solutions.

Findings

Effective in low distortion regimes

Achieves good rate-distortion performance

Complexity is manageable with discrete codes

Abstract

A general method of source coding over expansion is proposed in this paper, which enables one to reduce the problem of compressing an analog (continuous-valued source) to a set of much simpler problems, compressing discrete sources. Specifically, the focus is on lossy compression of exponential and Laplacian sources, which is subsequently expanded using a finite alphabet prior to being quantized. Due to decomposability property of such sources, the resulting random variables post expansion are independent and discrete. Thus, each of the expanded levels corresponds to an independent discrete source coding problem, and the original problem is reduced to coding over these parallel sources with a total distortion constraint. Any feasible solution to the optimization problem is an achievable rate distortion pair of the original continuous-valued source compression problem. Although finding the solution to this optimization problem at every distortion is hard, we show that our expansion coding scheme presents a good solution in the low distrotion regime. Further, by adopting low-complexity codes designed for discrete source coding, the total coding complexity can be tractable in practice.