Lossy compression of exponential and laplacian sources using expansion coding

A general method of source coding 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 Laplace sources, which are represented as set of discrete variables through a finite alphabet expansion. Due to the decomposability property of such sources, the resulting random variables post expansion are independent and discrete. Thus, these variables can be considered as independent discrete source coding problems, and the original problem is reduced to coding over these sources with a total distortion constraint. Any feasible solution to this resulting optimization problem corresponds to an achievable rate distortion pair of the original continuous-valued source compression problem. Although finding the optimal solution for a given distortion is not a tractable task, we show that, via a heuristic choice, our expansion coding scheme still presents a good performance in the low distortion regime. Further, by adopting low-complexity codes designed for discrete source coding, the total coding complexity can be reduced for practical implementations.