Consider a memoryless multiple source with m components of which a (possibly randomized) subset of k ≤ m components are sampled at each time instant and jointly compressed with the objective of reconstructing a prespecified subset of the m components under a given distortion criterion. The combined sampling and lossy compression mechanisms are to be designed to perform robustly with or without exact knowledge of the underlying joint probability distribution of the source. In this dissertation, we introduce a new framework of sampling rate distortion to study the tradeoffs among sampling mechanism, encoder-decoder structure, compression rate and the desired level of accuracy in the reconstruction.We begin with a discrete memoryless multiple source whose joint probability mass function (pmf) is taken to be known. A notion of sampling rate distortion function is introduced to study the mentioned tradeoffs, and is characterized first for fixed-set sampling. Next, for independent random sampling performed without the knowledge of the source outputs, it is shown that the sampling rate distortion function is the same whether or not the decoder is informed of the sequence of sampled sets. For memoryless random sampling, with the sampling depending on the source outputs, it is shown that deterministic sampling, characterized by a conditional point-mass, is optimal and suffices to achieve the sampling rate distortion function.Building on this, we consider a universal setting where the joint pmf of a discrete memoryless multiple source is known only to belong to a finite family of pmfs.In Bayesian and nonBayesian settings, single-letter characterizations are provided for the universal sampling rate distortion function for the fixed-set sampling, independent random sampling and memoryless random sampling. We show that these sampling mechanisms successively improve upon each other: (i) in their ability to enable an associated encoder approximate the underlying joint pmf and (ii) in their ability to choose appropriate subsets of the multiple source for compression by the encoder.Lastly, we consider a jointly Gaussian multiple memoryless source, to be reconstructed under a mean-squared error distortion criterion, with joint probability distribution function known only to belong to an uncountable family of probability density functions (characterized by a convex compact subset in Euclidean space).For fixed-set sampling, we characterize the universal sampling rate distortion function in Bayesian and nonBayesian settings. We also provide optimal reconstruction algorithms, of reduced complexity, which compress and reconstruct the sampled source components first under a modified distortion criterion, and then form MMSE estimates for the unsampled components based on reconstructions of the former. AcknowledgmentsThis dissertation started with a joint project between Prof. Prakash Narayan and Prof. Ankur Srivastava, as a principled way to studying an important problem in computer architecture. In multicore processors, an increase in...
Consider a discrete memoryless multiple source with m components of which k ≤ m possibly different sources are sampled at each time instant and jointly compressed in order to reconstruct all the m sources under a given distortion criterion. A new notion of sampling rate distortion function is introduced, and is characterized first for the case of fixed-set sampling. Next, for independent random sampling performed without knowledge of the source outputs, it is shown that the sampling rate distortion function is the same regardless of whether or not the decoder is informed of the sequence of sampled sets. Furthermore, memoryless random sampling is considered with the sampler depending on the source outputs and with an informed decoder. It is shown that deterministic sampling, characterized by a conditional point-mass, is optimal and suffices to achieve the sampling rate distortion function. For memoryless random sampling with an uninformed decoder, an upper bound for the sampling rate distortion function is seen to possess a similar property of conditional point-mass optimality. It is shown by example that memoryless sampling with an informed decoder can outperform strictly any independent random sampler, and that memoryless sampling can do strictly better with an informed decoder than without. Index TermsDiscrete memoryless multiple source, independent random sampler, memoryless random sampler, random sampling, rate distortion, sampling rate distortion function. † V.P. Boda and P. Narayan are with the
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