Design of Optimal Quantizers for Distributed Coding of Noisy Sources

Abstract

We investigate the design of optimal quantizers for individual encoding of several noisy observations of an unseen source, which is jointly decoded with the help of side information available at the decoder only. The joint statistics of the source data, the noisy observations and the side information are known, and exploited in the design. A variety of lossless coders for the quantization indices, including ideal Slepian-Wolf coders, are allowed. We present the optimality conditions such quantizers must satisfy, together with an extension of the Lloyd algorithm for a locally optimal design. Experimental results for Wyner-Ziv quantization of noisy Gaussian sources confirm the high-rate quantization theory established in our previous work.

High-rate quantization and transform coding with side information at the decoder

“…This is consistent with the experimental results of the application of the Lloyd algorithm for noisy WZ quantization design in [49].…”

“…Using Gaussian statistics and Mean-Squared Error (MSE) as a distortion measure, [13] proved that distributed coding of two noisy observations without side information can be carried out with a performance close to that of joint coding and denoising, in the limit of small distortion and large dimension. Most of the operational work on distributed coding of noisy sources, that is, for a fixed dimension, deals with quantization design for a variety of settings [46][47][48][49], but does not consider the characterization of such quantizers at high rates or transforms.…”

Network Distributed Quantization

“…We present a unified framework in which a variety of coding settings is allowed, including ideal SlepianWolf coding, along with an extension of the Lloyd algorithm for "locally" optimal design. This work builds upon the distributed coding problem studied in [27], by considering several decoders, and summarizes part of the research detailed in [28], where mathematical technicalities and proofs are provided.…”

A Generalization of the Rate-Distortion Function for Wyner-Ziv Coding of Noisy Sources in the Quadratic-Gaussian Case

“…For dimensions n = 1, 2, 3, noisy WZ quantizers q(z n ) and reconstruction functionsx n (q, y n ) were designed using an extension of the Lloyd algorithm for distributed source coding, described in [12], to noisy sources [13]. Such quantizers were designed assuming that the quantization index Q = q(Z n ) is losslessly coded with an ideal Slepian-Wolf coder at rate R = 1 n H(Q|Y n ).…”