By Topic

Noisy Constrained Capacity for BSC Channels

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)

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 input is a sequence from a constrained set. As stated by Fan , “... while calculation of the noise-free capacity of constrained sequences is well known, the computation of the capacity of a constraint in the presence of noise ... has been an unsolved problem in the half-century since Shannon's landmark paper.” We first express the constrained capacity of a binary symmetric channel with (d,k)-constrained input as a limit of the top Lyapunov exponents of certain matrix random processes. Then, we compute asymptotic approximations of the noisy constrained capacity for cases where the noise parameter ε is small. In particular, we show that when k ≤ 2d, the error term (excess of capacity beyond the noise-free capacity) is O(ε) , whereas it is O(εlogε) when k > 2d. In both cases, we compute the coefficient of the error term. In the course of establishing these findings, we also extend our previous results on the entropy of a hidden Markov process to higher-order finite memory processes. These conclusions are proved by a combination of analytic and combinatorial methods.

Published in:

IEEE Transactions on Information Theory  (Volume:56 ,  Issue: 11 )