Ph.D Thesis

Ph.D StudentSabbag Erez
SubjectTopics in Channel Reliability and Error Exponent Analysis
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROF. Neri Merhav


This thesis includes few results regarding error exponent analysis. We start with an information--theoretic approach to watermark embedding and detection under limited detector resources. First, we consider the attack-free scenario under which asymptotically optimal decision regions in the Neyman-Pearson sense are proposed, along with the optimal embedding rule. Later, we explore the case of zero-mean i.i.d.\ Gaussian covertext distribution with unknown variance under the attack-free scenario. For this case, we propose a lower bound on the exponential decay rate of the false-negative probability and prove that the optimal embedding and detecting strategy is superior to the customary linear, additive embedding strategy in the exponential sense. Finally, these results are extended to the case of memoryless attacks and general worst case attacks. Optimal decision regions and embedding rules are offered, and the worst attack channel is identified.

In the second part of the work, we consider a decoder with an erasure option and a variable size list decoder for channels with non-casual side information at the transmitter. First, universally achievable region of error exponents is offered for decoding with an erasure option using a parameterized decoder in the spirit of Csisz\'{a}r and K\"{o}rner's decoder. Then, the proposed decoding rule is generalized by extending the range of its parameters to allow variable size list decoding. This extension gives a unified treatment for erasure/list decoding. An achievable  region of exponential bounds on the probability of list error and the average number of incorrect messages on the list are given. Relations to Forney's and Csisz\'{a}r and K\"{o}rner's decoders for discrete memoryless channel are discussed. These results are obtained by exploring a random binning code with conditionally constant composition codewords proposed by Moulin and Wang, but with a different decoding rule and a modified analysis.

Finally, we analyze achievable random coding error exponents pertaining to erasure/list decoding for channels with side information present at the transmitter where the analysis is carried out using the \emph{optimal} decoding rule proposed by Forney. A key ingredient in the analysis is the evaluation of moments of a certain distance enumerator. This approach leads to a new exponentially tight bounds. These results are obtained by exploring a random binning code with conditionally constant composition codewords previously proposed by Moulin and Wang.