Ph.D Thesis | |

Ph.D Student | Weinberger Nir |
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Subject | Large Deviations Aspects in Coding Problems |

Department | Department of Electrical and Computer Engineering |

Supervisor | PROF. Neri Merhav |

We consider source coding and channel coding problems which exhibit trade-offs between different figures of merit. The main analysis tool is the method of large deviations analysis, incorporating its recently developed advanced methods, which were obtained by a statistical-mechanics point of view of random codes. First, motivated by on-line distributed source coding problems, we consider a variable-rate Slepian-Wolf source coding system, and characterize the optimal trade-off between the error exponent and the excess-rate exponent. Specifically, we show that the variable-rate code can assign the same rate to source vectors of the same empirical distribution (type), without degrading the exponents. Then, for a given requirement on the error exponent, we determine the optimal rate function, namely, the minimal rate possible for any given type, and derive the excess-rate exponent of this optimal rate function. Second, we consider a lossy source coding system, which operates in the presence of an eavesdropper, and characterize the optimal trade-off between the key-rate and exiguous-distortion exponent at the eavesdropper, under constraints on the coding-rate and the excess-distortion exponent at the legitimate decoder. Third, we consider a joint detection and channel coding problem, which arises in communication over time-varying channels and in communication systems with authentication requirements. We characterize the optimal joint detector/decoder, and provide an achievable region for the false-alarm exponent, the misdetection exponent, and the decoding error exponent. Specifically, the exact single-letter expression for the random coding exponents is found, as well as expurgated exponents.