Asymptotic Design of Quantizers for Decentralized MMSE Estimation

• Published in: IEEE transactions on signal processing Vol. 55; no. 11; pp. 5485 - 5496
• Main Authors: Marano, S., Matta, V., Willett, P.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Asymptotic properties; Coding, codes; Constraint theory; Counters; Decoding; Detection, estimation, filtering, equalization, prediction; Distributed estimation; Entropy; Estimating; Exact sciences and technology; high-resolution quantization; Inference; Information, signal and communications theory; Least mean squares algorithm; Mathematical analysis; Mean square error methods; Mean square errors; multiterminal inference; Nonuniform; Parameter estimation; Performance analysis; Quantization; Random variables; Rate-distortion; Sampling, quantization; Signal and communications theory; Signal, noise; Source coding; Telecommunications and information theory; Parameter estimation; High resolution; Source coding; System design; Entropy; Decoding; high-resolution quantization; Mean square error; Decentralized system; Signal quantization; multiterminal inference; Quantifier; Distributed estimation
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2007.898755

Conceptual and practical encoding/decoding, aimed at accurately reproducing remotely collected observations, has been heavily investigated since the pioneering works by Shannon about source coding. However, when the goal is not to reproduce the observables, but making inference about an embedded parameter and the scenario consists of many unconnected remote nodes, the landscape is less certain. We consider a multiterminal system designed for efficiently estimating a random parameter according to the minimum mean square error (MMSE) criterion. The analysis is limited to scalar quantizers followed by a joint entropy encoder, and it is performed in the high-resolution regime where the problem can be more easily mathematically tackled. Focus is made on the peculiarities deriving from the estimation task, as opposed to that of reconstruction, as well as on the multiterminal, as opposite to centralized, character of the inference. The general form of the optimal nonuniform quantizer is derived and examples are given.