Uncoded Transmission Is Exactly Optimal for a Simple Gaussian "Sensor" Network

• Published in: IEEE transactions on information theory Vol. 54; no. 11; pp. 5247 - 5251
• Main Author: Gastpar, M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Application software; Applied sciences; Codes; Coding, codes; Communication standards; Cut-set bound; Data transmission; Decoding; Detection, estimation, filtering, equalization, prediction; Digital communication; Engineering profession; Exact sciences and technology; Gaussian noise; Information theory; Information, signal and communications theory; joint source-channel coding; maximum correlation coefficient; Miscellaneous; Normal distribution; Random variables; Sensor fusion; Sensors; Signal and communications theory; Signal processing; Signal, noise; source-channel separation theorem; Telecommunication network reliability; Telecommunications and information theory; Correlation coefficient; Multiple access; joint source-channel coding; Parameter estimation; Source separation; Gaussian channel; Signal estimation; source-channel separation theorem; maximum correlation coefficient; Joint source channel coding; Mean square error; Optimal strategy; Gaussian noise; Cut-set bound; Signal processing; Sensor array; Multiple channel; Memoryless source; Signal detection
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2008.929967

A single memoryless Gaussian source is observed by many terminals, subject to independent Gaussian observation noises. The terminals are linked to a fusion center via a standard Gaussian multiple-access channel. The fusion center needs to recover the underlying Gaussian source with respect to mean-squared error. In this correspondence, a theorem of Witsenhausen is shown to imply that an optimal communication strategy is uncoded transmission, i.e., each terminal's channel input is merely a scaled version of its noisy observation.