Distributed Estimation and Coding: A Sequential Framework Based on a Side-Informed Decomposition

Abstract

We propose a sequential framework for the distributed multiple-sensor estimation and coding problem that decomposes the problem into a series of side-informed source coding problems and enables construction of good codecs. Our construction relies on a separation result for the simplified scenario where information from one sensor is to be sent to the CP that already has information regarding the desired signal. We show that the optimal encoder decoder combination, in this setting, can be decomposed, without loss in performance, into two steps: A first preprocessing step to extract relevant information from the indirect observation with consideration of the side information, followed by a second step of side-informed encoding of the preprocessed output. A recursive exploit of the decomposition coupled with side-informed transform coding allows us to construct encoders by reusing scalar Wyner-Ziv codecs. We develop a numerical procedure for obtaining bounds delineating the best achievable performance for the proposed sequential framework and construct and demonstrate a practical codec in the proposed framework that achieves empirical performance close to the bound. Furthermore, we also compare the bounds for the sequential scheme against bounds for a number of alternate schemes-for some of which codec constructions are obvious and others for which codec constructions are inobvious. Our results show that, in most cases, our codec exceeds the performance bound of schemes offering obvious constructions. The achievable bound for our sequential framework is also shown to be close to a general nonconstructive distributed bound that does not impose the sequential constraint indicating that the sequential approach may not cause a significant performance compromise.