|Stochastic Systems Group|
Digital Signal Processing Group
Research Lab for Electronics
While the fundamental performance limits of point-to-point communication are well understood (thanks to Shannon), this is not true for network communication. A major stumbling block is how to deal with correlations between messages. If we ignore correlations, our design will be suboptimal, but we do not always know how to take advantage of correlations. To begin to explore these issues we focus on two classes of sensor network.
In the first class, L geographically-dispersed sensors observe independently-corrupted versions of a common source signal. They communicate data subject to a total rate constraint R back to a central data-fusion site, which integrates the messages to make a source estimate. In information theory this is called the CEO problem. In the second class, the L sensors are ordered and communicate --- one to the next --- over rate-constrained links, with only the final sensor in the chain communicating directly with the CEO. We call this the sequential CEO problem. In both cases our objective is to minimize the CEO's distortion subject to the total rate constraint.
Our approach to these problems involves first generalizing Wyner-Ziv source coding with side information to noisy encoder observations, which we characterize in the binary-Hamming and Gaussian-quadratic cases. We then show how the sequential CEO problem can be approached as a cascade of noisy Wyner-Ziv stages, and how a dual formulation leads naturally to a sequentially-structured coding strategy for the regular CEO problem.
For the Gaussian-quadratic cases we present simple iterative (in L) achievable distortion-rate expressions, both for the sequential and regular CEO problems. For the latter, we fully analyze the L=2 and L \rightarrow \infty cases, showing that the regions achieved in these cases are the complete achievable regions. Furthermore, the results for L \rightarrow \infty are consistent with the rate-distortion results presented in Oohama '98.
Finally, we discuss how these solutions can be applied to the problem of relay communications.
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