Cascade multiterminal source coding

TL;DR

This paper studies the limits of distributed source coding in a cascade network for correlated sources, providing bounds on rates for lossy and lossless reconstruction, with specific insights for Gaussian sources.

Contribution

It introduces inner and outer bounds on the rate region for cascade multiterminal source coding with arbitrary distortion functions, including a threshold analysis for Gaussian sources.

Findings

Inner and outer bounds on achievable rate regions are established.

A threshold is identified for optimal encoding strategies in Gaussian cases.

Relaying can outperform recompression depending on source variances.

Abstract

We investigate distributed source coding of two correlated sources X and Y where messages are passed to a decoder in a cascade fashion. The encoder of X sends a message at rate R_1 to the encoder of Y. The encoder of Y then sends a message to the decoder at rate R_2 based both on Y and on the message it received about X. The decoder's task is to estimate a function of X and Y. For example, we consider the minimum mean squared-error distortion when encoding the sum of jointly Gaussian random variables under these constraints. We also characterize the rates needed to reconstruct a function of X and Y losslessly. Our general contribution toward understanding the limits of the cascade multiterminal source coding network is in the form of inner and outer bounds on the achievable rate region for satisfying a distortion constraint for an arbitrary distortion function d(x,y,z). The inner bound makes use of a balance between two encoding tactics--relaying the information about X and recompressing the information about X jointly with Y. In the Gaussian case, a threshold is discovered for identifying which of the two extreme strategies optimizes the inner bound. Relaying outperforms recompressing the sum at the relay for some rate pairs if the variance of X is greater than the variance of Y.