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Information Rates of Densely Sampled Data: Distributed Vector Quantization and Scalar Quantization With Transforms for Gaussian sources

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IEEE TRANSACTIONS ON INFORMATION THEORY 2013年第9期59卷 5641-5664页

作者： Neuhoff, David L. Pradhan, S. Sandeep Univ Michigan Dept Elect Engn & Comp Sci Ann Arbor MI 48109 USA

This paper establishes rates attainable by several lossy schemes for coding a continuous parameter source to a specified mean-squared-error distortion based on sampling at asymptotically large rates. First, a densely sampled, spatiotemporal, stationary Gaussian source is distributively encoded. The Berger-Tung bound to the distributed rate-distortion function and three convergence theorems are used to obtain an upper bound, expressed in terms of the source spectral density, to the smallest attainable rate at asymptotically large sampling rates. The bound is tighter than that recently obtained by Kashyap et al. Both indicate that with ideal distributed lossy coding, dense sensor networks can efficiently sense and convey a field, in contrast to the negative result obtained by Marco et al. for encoders based on scalar quantization and Slepian-Wolf distributed lossless coding. The second scheme is transform coding with scalar coefficient quantization. A new generalized transform coding analysis, as well as the aforementioned convergence theorems, is used to find the smallest attainable rate at asymptotically large sampling rates in terms of the source spectral density and the operational rate-distortion function of the family of quantizers, which in contrast to previous analyses need not be convex. The result shows that when a transform is used, scalar quantization need not cause the poor performance found by Marco et al. As a corollary, the final result pursues an approach, originally proposed by Berger, to show that the inverse water-pouring formula for the rate-distortion function can be attained at high sampling rates by transform coding with ideal vector quantization to encode the coefficients. Also established in the paper are relations between operational rate-distortion and distortion-rate functions for a continuous parameter source and those for the discrete parameter source that results from sampling.

关键词： continuous-time source coding distributed source coding lossy source coding oversampling rate-distortion theory transform coding

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