Successive Wyner-Ziv Coding Scheme and its Application to the Quadratic Gaussian CEO Problem

We introduce a distributed source coding scheme called successive Wyner-Ziv coding. We show that any point in the rate region of the quadratic Gaussian CEO problem can be achieved via the successive Wyner-Ziv coding. The concept of successive refinement in the single source coding is generalized to the distributed source coding scenario, which we refer to as distributed successive refinement. For the quadratic Gaussian CEO problem, we establish a necessary and sufficient condition for distributed successive refinement, where the successive Wyner-Ziv coding scheme plays an important role.Comment: 28 pages, submitted to the IEEE Transactions on Information Theor

Erasure Multiple Descriptions

We consider a binary erasure version of the n-channel multiple descriptions problem with symmetric descriptions, i.e., the rates of the n descriptions are the same and the distortion constraint depends only on the number of messages received. We consider the case where there is no excess rate for every k out of n descriptions. Our goal is to characterize the achievable distortions D_1, D_2,...,D_n. We measure the fidelity of reconstruction using two distortion criteria: an average-case distortion criterion, under which distortion is measured by taking the average of the per-letter distortion over all source sequences, and a worst-case distortion criterion, under which distortion is measured by taking the maximum of the per-letter distortion over all source sequences. We present achievability schemes, based on random binning for average-case distortion and systematic MDS (maximum distance separable) codes for worst-case distortion, and prove optimality results for the corresponding achievable distortion regions. We then use the binary erasure multiple descriptions setup to propose a layered coding framework for multiple descriptions, which we then apply to vector Gaussian multiple descriptions and prove its optimality for symmetric scalar Gaussian multiple descriptions with two levels of receivers and no excess rate for the central receiver. We also prove a new outer bound for the general multi-terminal source coding problem and use it to prove an optimality result for the robust binary erasure CEO problem. For the latter, we provide a tight lower bound on the distortion for \ell messages for any coding scheme that achieves the minimum achievable distortion for k messages where k is less than or equal to \ell.Comment: 48 pages, 2 figures, submitted to IEEE Trans. Inf. Theor

Source Coding in Networks with Covariance Distortion Constraints

We consider a source coding problem with a network scenario in mind, and formulate it as a remote vector Gaussian Wyner-Ziv problem under covariance matrix distortions. We define a notion of minimum for two positive-definite matrices based on which we derive an explicit formula for the rate-distortion function (RDF). We then study the special cases and applications of this result. We show that two well-studied source coding problems, i.e. remote vector Gaussian Wyner-Ziv problems with mean-squared error and mutual information constraints are in fact special cases of our results. Finally, we apply our results to a joint source coding and denoising problem. We consider a network with a centralized topology and a given weighted sum-rate constraint, where the received signals at the center are to be fused to maximize the output SNR while enforcing no linear distortion. We show that one can design the distortion matrices at the nodes in order to maximize the output SNR at the fusion center. We thereby bridge between denoising and source coding within this setup