Ph.D Thesis


Ph.D StudentWeinberger Nir
SubjectLarge Deviations Aspects in Coding Problems
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROF. Neri Merhav


Abstract

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.