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New bounds on the entropy rate of hidden Markov processes

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2 Author(s)
Ordentlich, E. ; HP Labs., Palo Alto, CA, USA ; Weissman, T.

Let {Xt} be a stationary finite-alphabet Markov chain and {Zt} denote its noisy version when corrupted by a discrete memoryless channel. Let P(Xt∈·|Z-∞t) denote the conditional distribution of Xt given all past and present noisy observations, a simplex-valued random variable. We present a new approach to bounding the entropy rate of {Zt} by approximating the distribution of this random variable. This approximation is facilitated by the construction and study of a Markov process whose stationary distribution determines the distribution of P(Xt∈·|Z-∞t). To illustrate the efficacy of this approach, we specialize it and derive concrete bounds for the case of a binary Markov chain corrupted by a binary symmetric channel (BSC). These bounds are seen to capture the behavior of the entropy rate in various asymptotic regimes.

Published in:

Information Theory Workshop, 2004. IEEE

Date of Conference:

24-29 Oct. 2004

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