Efficient LDPC Codes over GF(q) for Lossy Data Compression

In this paper we consider the lossy compression of a binary symmetric source. We present a scheme that provides a low complexity lossy compressor with near optimal empirical performance. The proposed scheme is based on b-reduced ultra-sparse LDPC codes over GF(q). Encoding is performed by the Reinforced Belief Propagation algorithm, a variant of Belief Propagation. The computational complexity at the encoder is O(.n.q.log q), where is the average degree of the check nodes. For our code ensemble, decoding can be performed iteratively following the inverse steps of the leaf removal algorithm. For a sparse parity-check matrix the number of needed operations is O(n).Comment: 5 pages, 3 figure

Lossy Compression of Exponential and Laplacian Sources using Expansion Coding

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.Comment: 8 pages, 3 figure