Asymptotics of input-constrained binary symmetric channel capacity

Abstract

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.

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

References in corpus (2)

• The Entropy of a Binary Hidden Markov Process
• From finite-system entropy to entropy rate for a Hidden Markov Process

Cited by in corpus (7)

• Asymptotics of Input-Constrained Erasure Channel Capacity
• Analyticity of Entropy Rate of Continuous-State Hidden Markov Chains
• Extensions of the I-MMSE Relation
• A Randomized Approach to the Capacity of Finite-State Channels
• Concavity of Mutual Information Rate for Input-Restricted Finite-State Memoryless Channels at High SNR
• Extensions of the I-MMSE Relationship to Gaussian Channels with Feedback and Memory
• Limit Theorems in Hidden Markov Models