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Extremal Problems of Error Exponents and Capacity of Duplication Channels Open Access


Other title
binary symmetric channel (BSC)
binary erasure channel (BEC)
set of basis channels
Chebychev systems
random-coding error exponent
channels with synchronization errors
memoryless binary-input symmetric-output channels
channel dispersion
error exponents
information theory
capacity expansion
channel reliability function
insertion/deletion channels
symmetric channels
duplication channels
Type of item
Degree grantor
University of Alberta
Author or creator
Ramezani, Mahdi
Supervisor and department
Ardakani, Masoud (Electrical and Computer Engineering)
Examining committee member and department
Tellambura, Chintha (Electrical and Computer Engineering)
Jiang, Hai (Electrical and Computer Engineering)
Kouritzin, Michael (Mathematical and Statistical Sciences)
Alajaji, Fady (Department of Mathematics and Statistics, Queen's University)
Department of Electrical and Computer Engineering
Date accepted
Graduation date
Doctor of Philosophy
Degree level
One of the most stunning results of information theory is the channel coding theorem addressing the maximum rate of reliable communication over a noisy channel, known as channel capacity. In this thesis, we consider two problems emerging from the classic channel coding theorem. First, we study the extremal problems of the channel reliability function, which is the exponent with which the probability of making a wrong decision vanishes. To this end, we introduce a set of fundamental channels which exhibit significant monotonicity properties and invoke the theory of Chebychev systems to utilize such properties. We show that the binary symmetric channel (BSC) and binary erasure channel (BEC), which happen to be among the fundamental channels, are the two extremes of the channel reliability function. Also, we show that given a rate and a probability of error as a performance measure, BSC (BEC) needs the longest (shortest) code length to achieve such performance. While the first problem is pure theoretical, the second problem addresses a challenging practical scenario. The most fundamental assumption in the classic channel coding theorem is that we receive as many symbols as we send. In reality, however, this is not always true, e.g., a miss-sampling at a conventional receiver might duplicate a symbol. The extra symbol confuses a receiver as it has no clue about the position of duplication. Such scenarios are collectively known as channels with synchronization errors. Unlike their classic counterparts, there is only little known about either the capacity or coding techniques for channels with synchronization errors, even in their simplest forms. In this part, we study the duplication channel by introducing a series expansion for its capacity.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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