No abstract

The source-coding problem with side information at the decoder is studied subject to a constraint that the encoderto whom the side information is unavailable-be able to compute the decoder's reconstruction sequence to within some distortion.For discrete memoryless sources and finite single-letter distortion measures, an expression is given for the minimal description rate as a function of the joint law of the source and side information and of the allowed distortions at the encoder and at the decoder. The minimal description rate is also computed for a memoryless Gaussian source with squared-error distortion measures.A solution is also provided to a more general problem where there are more than two distortion constraints and each distortion function may be a function of three arguments: the source symbol, the encoder's reconstruction symbol, and the decoder's reconstruction symbol.

International audienceA source generates a point pattern consisting of a finite number of points in an interval. Based on a binary description of the point pattern, a reconstructor must produce a covering set that is guaranteed to contain the pattern. We study the optimal tradeoff (as the length of the interval tends to infinity) between the description length and the least average Lebesgue measure of the covering set. The tradeoff is established for point patterns that are generated by homogeneous and inhomogeneous Poisson processes. The homogeneous Poisson process is shown to be the most difficult to describe among all point patterns. We also study a Wyner-Ziv version of this problem, where some of the points in the pattern are revealed to the reconstructor but not to the encoder. We show that this scenario is as good as when they are revealed to both encoder and reconstructor. A connection between this problem and the queueing distortion is established via feedforward. Finally, we establish the aforementioned tradeoff when the covering set is allowed to miss some of the points in the pattern at a certain cost

An encoder observes a point pattern-a finite number of points in the interval [0, T ]-which is to be described to a reconstructor using bits. Based on these bits, the reconstructor wishes to select a subset of [0, T ] that contains all the points in the pattern. It is shown that, if the point pattern is produced by a homogeneous Poisson process of intensity λ, and if the reconstructor is restricted to select a subset of average Lebesgue measure not exceeding DT , then, as T tends to infinity, the minimum number of bits per second needed by the encoder is −λ log D. It is also shown that, as T tends to infinity, any point pattern on [0, T ] containing no more than λT points can be successfully described using −λ log D bits per second in this sense. Finally, a Wyner-Ziv version of this problem is considered where some of the points in the pattern are known to the reconstructor.

Abstract-We generalize the Wyner-Ziv source coding problem with side-information at the decoder to the case where the encoder is required to be able to compute the decoder's reconstruction sequence with some fidelity. This requirement limits the extent to which the reconstruction sequence can depend on the side-information, which is not available to the encoder.For finite-alphabet memoryless sources and single-letter distortion measures we compute the minimal description rate as a function of the joint law of the source and side-information and of the allowed distortions at the encoder and decoder. We also treat memoryless Gaussian sources with mean squared-error distortion measures.