2 research outputs found

    Rate-Distortion Function for a Heegard-Berger Problem with Two Sources and Degraded Reconstruction sets

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    In this work, we investigate an instance of the Heegard-Berger problem with two sources and arbitrarily correlated side information sequences at two decoders, in which the reconstruction sets at the decoders are degraded. Specifically, two sources are to be encoded in a manner that one of the two is reproduced losslessly by both decoders, and the other is reproduced to within some prescribed distortion level at one of the two decoders. We establish a single-letter characterization of the rate-distortion function for this model. The investigation of this result in some special cases also sheds light on the utility of joint compression of the two sources. Furthermore, we also generalize our result to the setting in which the source component that is to be recovered by both users is reconstructed in a lossy fashion, under the requirement that all terminals (i.e., the encoder and both decoders) can share an exact copy of the compressed version of this source component, i.e., a common encoder-decoders reconstruction constraint. For this model as well, we establish a single-letter characterization of the associated rate-distortion function.Comment: Submitted to IEEE Trans. on Information Theor

    Function Computation over Networks:Efficient Information Processing for Cache and Sensor Applications

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    This thesis looks at efficient information processing for two network applications: content delivery with caching and collecting summary statistics in wireless sensor networks. Both applications are studied under the same paradigm: function computation over networks, where distributed source nodes cooperatively communicate some functions of individual observations to one or multiple destinations. One approach that always works is to convey all observations and then let the destinations compute the desired functions by themselves. However, if the available communication resources are limited, then revealing less unwanted information becomes critical. Centered on this goal, this thesis develops new coding schemes using information-theoretic tools. The first part of this thesis focuses on content delivery with caching. Caching is a technique that facilitates reallocation of communication resources in order to avoid network congestion during peak-traffic times. An information-theoretic model, termed sequential coding for computing, is proposed to analyze the potential gains offered by the caching technique. For the single-user case, the proposed framework succeeds in verifying the optimality of some simple caching strategies and in providing guidance towards optimal caching strategies. For the two-user case, five representative subproblems are considered, which draw connections with classic source coding problems including the Gray-Wyner system, successive refinement, and the Kaspi/Heegard-Berger problem. Afterwards, the problem of distributed computing with successive refinement is considered. It is shown that if full data recovery is required in the second stage of successive refinement, then any information acquired in the first stage will be useful later in the second stage. The second part of this thesis looks at the collection of summary statistics in wireless sensor networks. Summary statistics include arithmetic mean, median, standard deviation, etc, and they belong to the class of symmetric functions. This thesis develops arithmetic computation coding in order to efficiently perform in-network computation for weighted arithmetic sums and symmetric functions. The developed arithmetic computation coding increases the achievable computation rate from Θ((logL)/L)\Theta((\log L)/L) to Θ(1/logL)\Theta(1/\log L), where LL is the number of sensors. Finally, this thesis demonstrates that interaction among sensors is beneficial for computation of type-threshold functions, e.g., the maximum and the indicator function, and that a non-vanishing computation rate is achievable
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