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An Application of Repeated Games in Network Information Theory

Delgosha, Payam | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45881 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Aminzadeh Gohari, Amin
  7. Abstract:
  8. Information Theory, as an important part of communication theory, tries to find inner and outer bounds for reliable rate of information transmission in communication networks. In Network Information Theory, It is usually assumed that the channel statistics is known to everyone. However, in some practical situations, we might not know the statistics. The compound channel and the arbitrarily varying channel (AVC) are two categories of models which have considered this problem. In this thesis, in order to have a more general model regarding information transfer in the presence of channel uncertainty, we propose a model which is essentially a combination of compound channel and AVC. In our model, channel dynamics is not only dependent on the inputs of an adversary, but also is dependent on a channel state parameter which is constant throughout the transmission. This state is unknown, but we assume that encoder, decoder and adversary have side information about it. Also in our model, we assume that both encoder and decoder observe adversary’s inputs causally. Such a challenge appears in a wider range of problems in which a limited resource (e.g. bandwidth) is going to be divided and parties are unaware of the exact state..The trade-off between usage of the side information (which results in a better usage of the channel) and other parties getting aware of such information (who might use them against each other) plays the key role in such problems.In Game Theory, similar problems are studied under the topic “Repeated Games”.Motivated by the above discussion, employing this field of Game Theory for analyzing the above category of problems seems reasonable. Therefore, it seems that a combination of methods from Game Theory and Information Theoretic tools, which have been used for such problems so far, can result in a better understanding of the flow of information and its role in these problems.In this thesis, we generalize the current results in repeated games from the “average” criteria to the “high probability” criteria. Afterwards, using these results and good strategies found in an auxiliary repeated game, we derive the capacity of our communication model. The game nature of the communication comes from the fact the the encoder can observe adversary’s input, hence he should adapt his coding strategy to these observations
  9. Keywords:
  10. Repeated Game ; Network Information Theory ; Arbitrarily Varying Channels (AVC) ; Adversary (Jammer)

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