Quadratic Gaussian Source Research Articles

A Strong Entropy Power Inequality

When one of the random summands is Gaussian, we sharpen the entropy power inequality (EPI) in terms of the strong data processing function for Gaussian channels. Among other consequences, this ‘strong’ EPI generalizes the vector extension of Costa’s EPI to non-Gaussian channels in a precise sense. This leads to a new reverse EPI and, as a corollary, sharpens Stam’s uncertainty principle relating entropy power and Fisher information (or, equivalently, Gross’ logarithmic Sobolev inequality). Applications to network information theory are also given, including a short self-contained proof of the rate region for the two-encoder quadratic Gaussian source coding problem and a new outer bound for the one-sided Gaussian interference channel.

New Coding Schemes for the Symmetric $K$-Description Problem

We propose novel coding schemes for the K-description problem with symmetric rates and symmetric distortion constraints. There are two main new ingredients in these schemes: the first one is akin to the method seen in the well-known butterfly network of network coding literature, and systematic erasure channel codes are applied on certain carefully chosen source coding component; the second approach is built on the quantization splitting technique which was previously proven useful in the Gaussian CEO problem. We first focus on a special case of the three description problem, where any two descriptions are rate-distortion optimal jointly, referred to as the no two description excess rate case. For this special case and the quadratic Gaussian source, we show that the two aforementioned approaches lead to rate-distortion points outside the achievable region based on the source-channel erasure codes, previously proposed by Pradhan, Puri, and Ramchandran. Interestingly, though only the symmetric problem is considered in our work, the proposed schemes in fact benefit from time-sharing several asymmetric rate-distortion points. The insights gained through the no two description excess rate case lead to strategic combination of the new ingredients with the existing coding scheme, yielding new coding schemes for the symmetric K -description problem.

Side-Information Scalable Source Coding

We consider the problem of side-information scalable (SI-scalable) source coding, where the encoder constructs a two-layer description, such that the receiver with high quality side information will be able to use only the first layer to reconstruct the source in a lossy manner, while the receiver with low quality side information will have to receive both layers in order to decode. We provide inner and outer bounds to the rate-distortion (R-D) region for general discrete memoryless sources. The achievable region is tight when either one of the decoders requires a lossless reconstruction, and when the distortion measures are degraded and deterministic. Furthermore, the gap between the inner and the outer bounds can be bounded by certain constants when the squared error distortion measure is used. The notion of perfect scalability is introduced, for which necessary and sufficient conditions are given for sources satisfying a mild support condition. Using SI-scalable coding and successive refinement Wyner-Ziv coding as basic building blocks, we provide a complete characterization of the rate-distortion region for the important quadratic Gaussian source with multiple jointly Gaussian side informations, where the side information quality is not necessarily monotonic along the scalable coding order. A partial result is provided for the doubly symmetric binary source under the Hamming distortion measure when the worse side information is a constant, for which one of the outer bounds is strictly tighter than the other.