On the deletion channel with small deletion probability

Details On the deletion channel with small deletion probability On the deletion channel with small deletion probability

2009-12-29

arxiv.org/abs/0912.5176v3

IEEE Intl. Symp. Information Theory Proc. (2010) 1002-1006

Computer Science

Information Theory

5 pages, 1 figure v3: minor corrections

Scientific paper

The deletion channel is the simplest point-to-point communication channel that models lack of synchronization. Despite significant effort, little is known about its capacity, and even less about optimal coding schemes. In this paper we intiate a new systematic approach to this problem, by demonstrating that capacity can be computed in a series expansion for small deletion probability. We compute two leading terms of this expansion, and show that capacity is achieved, up to this order, by i.i.d. uniform random distribution of the input. We think that this strategy can be useful in a number of capacity calculations.

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