Asymptotics of input-constrained binary symmetric channel capacity

Details Asymptotics of input-constrained binary symmetric channel capacity Asymptotics of input-constrained binary symmetric channel capacity

2008-03-24

arxiv.org/abs/0803.3360v3

Annals of Applied Probability 2009, Vol. 19, No. 3, 1063-1091

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP570 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/08-AAP570

We study the classical problem of noisy constrained capacity in the case of the binary symmetric channel (BSC), namely, the capacity of a BSC whose inputs are sequences chosen from a constrained set. Motivated by a result of Ordentlich and Weissman [In Proceedings of IEEE Information Theory Workshop (2004) 117--122], we derive an asymptotic formula (when the noise parameter is small) for the entropy rate of a hidden Markov chain, observed when a Markov chain passes through a BSC. Using this result, we establish an asymptotic formula for the capacity of a BSC with input process supported on an irreducible finite type constraint, as the noise parameter tends to zero.

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