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New Approaches for Achievability Proof in Network Information Theory: Asymptotic Regime and Beyond

Yassaee, Mohammad Hossein | 2015

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 44201 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Aref, Mohammad Reza
  7. Abstract:
  8. Two new frameworks for achievability proof in network information theory (NIT) are introduced . The first framework which we call it OSRB (Output Statistics of Random Binning) framework, uses random binning arguments and is based on a duality between channel and source coding problems. Furthermore, the OSRB framework uses pmf approximation arguments instead of counting and typicality which are used widely in conventional achievability proofs in NIT. This allows for proving coordination and strong secrecy problems, where certain statistical conditions on the
    distribution of random variables need to be satisfied. These statistical conditions include independence between messages and eavesdropper’s observations in secrecy problems and closeness to a certain distribution (usually, i.i.d. distribution) in coordination problems. One important feature of the framework is to enable one to add an eavesdropper and obtain a result on the secrecy rates for free. We make a case for generality of the framework by studying examples in the variety of settings containing channel coding, lossy source coding, joint source-channel coding, coordination, strong secrecy, feedback, and relaying. In particular, by investigating the framework for the lossy source coding problem over broadcast channel, it is shown that the new framework provides a simple alternative scheme to hybrid coding scheme. In addition, new results on secrecy rate region (under strong secrecy criterion) of wiretap broadcast channel and wiretap relay channel are derived.
    One of the main grounds for the OSRB framework is the channel simulation problems. We show the usefulness of the OSRB framework by applying it to the problem of channel simulation via interactive communications to derive new inner region for this problem. Furthermore, the optimality of this region is shown by using
    an appropriate converse proof. Next, a novel achievability proof technique is introduced for NIT problems in One-Shot regime. The technique is not based on covering and packing lemmas. This technique uses stochastic coders with a particular structure for coding that resembles both the ML and the joint-typicality coders. Although stochastic encoders and decoders do not usually enhance the capacity region, their use simplifies the analysis. The Jensen inequality lies at the center of error analysis, which enables us to deal with the expectation of many terms coming from stochastic encoders and decoders at once. The results of this techniques resemble the corresponding results in the asymptotic regime. Further, the results can be employed to get results for finite block-length regime
  9. Keywords:
  10. Network Information Theory

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