M.Sc Thesis

M.Sc StudentBerger Liat
SubjectEncoding and Decoding under Channel Uncertainty
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROF. Neri Merhav


In this work, we address the problem of digital communication over a memoryless additive Gaussian channel with an unknown gain, which is a special, yet basic and important, case of a fading channel.

Clearly, in the presence of channel uncertainty, the optimal maximum likelihood (ML) decoder cannot be applied. A universal decoder which is commonly applied in this situation is the Generalized Likelihood Ratio Test (GLRT) decoder.

In a recent work, a universal minimax decoder was proposed, which minimizes the worst-case ratio between the error probability of a decoder that is independent of the unknown parameters and the minimum error probability associated with the ML decoder, given the parameters.

The present work is a continuation of this work, and its main purpose is to investigate the asymptotic performance of the universal minimax decoder, to outline the way it might be chosen, and to compare its performance with the GLRT decoder performance, for the memoryless Gaussian channel.

The analysis of  the two-codewords case, provides insight into the metric associated with the minimax decoder. Particularly, we demonstrate that when the codewords are of unequal energies, the optimal minimax decoder is superior to the GLRT decoder.

Zero-rate codes are analyzed, using the random coding approach.The average performance of the minimax decoder over two ensembles are studied. The analysis enables an explicit choice of a universal minimax decoder, which guarantees better average performance than that of the GLRT decoder, for each channel in the family. Comparison of the results for both ensembles, leads to a general conclusion about the existence of a better than GLRT minimax decoder, for zero-rate code ensembles that contain codewords with unequal energies. Finally, the results are partially extended to the positive-rate Gaussian ensemble.