Suppose a spatially distributed random field, such as temperature, is sampled by a network of densely spaced wireless sensors, and suppose these samples must be encoded for transmission to a common collector, where the field is reconstructed and displayed. We consider the following scaling question: What happens to the number of encoded bits per unit area, i.e. the encoding rate, as sensor density increases, given a quality of the decoded reconstruction? On the one hand, as density increases more sensor values must be encoded. On the other hand, adjacent values become more correlated, which might make it possible to limit the encoding rate from growing. A key issue is that each encoder must operate without access to the (correlated) outputs of other sensors, since they are not co-located. Thus, the quantization and encoding must be of the type called "distributed". In this talk, we analyze the scaling of two "extreme" schemes. The first uses elementary scalar quantization followed by ideal Slepian-Wolf distributed lossless source coding, and the analysis reduces to a classic question regarding the number of bits/second produced by scalar quantization and entropy coding. The second uses ideal distributed lossy coding, and the analysis involves the Berger-Tung bound and the Grenander-Szego asymptotic eigenvalue theory. Although in a conventional setting, scalar quantization with entropy coding yields rate-distortion performance close to that of ideal lossy coding, it turns out that in the high-sampling-rate distributed-coding context relevant to dense sensor networks, their performances are dramatically different.

David L. Neuhoff received the B.S.E. from Cornell, and the M.S. and Ph.D. in Electrical Engineering from Stanford. In 1974, he joined the University of Michigan, where he is now the Joseph E. and Anne P. Rowe Professor of Electrical Engineering. From 1984-1989 he was Associate Chair of the Systems Science and Engineering Division of the EECS Department. He spent two sabbaticals at Bell Laboratories, Murray Hill, NJ. His research and teaching interests are in communications, information theory, and signal processing, especially data compression, quantization, image and video coding, source-channel coding, data synchronization, halftoning, and distributed coding for sensor networks. Dr. Neuhoff is a Fellow of the IEEE, and First Vice President of the IEEE Information Theory Society.