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Evaluating the Rate of Compressibility of Sparse Stochastic Processes

Ghourchian, Hamid | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 48907 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Amini, Arash; Aminzadeh Gohari, Amin
  7. Abstract:
  8. In most stochastic models with uncountable cardinality of sample space with non-trivial probability measures, the inherent information is infinite. The continuous-valued random variables and continuous-domain random processes are among such objects. Therefore, a fidelity criterion must be defined between the stochastic subject and its estimated version. Although there are some criteria for of stochastic continuous signals, based on quantizing the signal in both time and amplitude domains, we are going to define a criterion which is for stochastic processes in bounded time domain. Next, the criterion will be expressed in general sources perspective and the optimum rate of coding will be found. Afterwards, we will calculate the criterion for sparse stochastic processes, especially compound Poisson processes and white stable noises. Moreover, it is shown that compound Poisson processes are more compressible that white stable noises, which is consistent with some previous criteria in compressibility of random processes. We define a well-defined space of random variables, (α,m,v)-AC, in which the differential entropy of distributions is uniformly continuous with respect to total variation of probability distributions. This space contains the absolutely random variables which have at least one bounded positive moment and bounded probability distribution. The benefit of this new space is that, it includes most of the previous spaces defined for convergence of differential entropy
  9. Keywords:
  10. Source Coding ; Random Variables ; Compression Ratio ; White Noise ; Poisson Process ; Sparse Stochastic Processes ; Differential Entropy Continuity ; White Stable Noise

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