Communication over channels with symbol synchronization errors

Synchronization is a problem of fundamental importance for a wide range of practical communication systems including reading media, multi-user optical channels, synchronous digital communication systems, packet-switched communication networks, distributed computing systems, etc. In this thesis I study various aspects of communication over channels with symbol synchronization errors. Symbol synchronization errors are harder to model than erasures or substitution errors caused by additive noise because they introduce uncertainties in timing. Consequently, the capacity of channels subjected to synchronization errors is a very challenging problem, even when considering the simplest channels for which only deletion errors occur. I improve on the best existing lower and upper bounds for the capacity of the deletion channel using convex and stochastic optimization techniques. I also show that simply finding closed-form expressions for the number of subsequences when deleting symbols from a string is computationally prohibitive. Constructing efficient synchronization error-correcting codes is also a challenging task. The main result of the thesis is the design of a new family of codes able to correct several types of synchronization errors. The codes use trellis and modified versions of the Viterbi decoding algorithm, and therefore have very low encoding and decoding complexities. They also have high data rates and work for reasonably noisy channels, which makes them one of the first synchronization-correcting codes that have any chance of being used in practical systems. In the last part of the thesis, I show that a synchronization approach can solve the opportunistic spectrum access problem in cognitive radio, where cognitive users want to communicate in presence of legacy users to whom the bandwidth has been licensed. I also consider the amount of communication required to solve a large class of distributed problems where synchronization errors can occur. More precisely, I study how allowing the parties to solve the problems incorrectly with small probability can reduce the total amount of communication or the number of messages that need to be exchanged.

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