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85
Hidden Markov processes
 IEEE Trans. Inform. Theory
, 2002
"... Abstract—An overview of statistical and informationtheoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discretetime finitestate homogeneous Markov chain observed through a discretetime memoryless invariant channel. In recent years, the work of Baum and Petrie on finite ..."
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Cited by 264 (5 self)
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Abstract—An overview of statistical and informationtheoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discretetime finitestate homogeneous Markov chain observed through a discretetime memoryless invariant channel. In recent years, the work of Baum and Petrie on finite
Entropy rate of continuousstate hidden Markov chains
 IEEE ISIT
"... AbstractWe prove that under mild positivity assumptions, the entropy rate of a continuousstate hidden Markov chain, observed when passing a finitestate Markov chain through a discretetime continuousoutput channel, is analytic as a function of the transition probabilities of the underlying Mark ..."
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Cited by 2 (2 self)
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AbstractWe prove that under mild positivity assumptions, the entropy rate of a continuousstate hidden Markov chain, observed when passing a finitestate Markov chain through a discretetime continuousoutput channel, is analytic as a function of the transition probabilities of the underlying
On the Entropy of a Hidden Markov Process
 Proceedings of the Data Compression Conference, Snowbird
, 2004
"... We study the entropy rate of a binary hidden Markov process (HMP) defined by observing the output of a binary symmetric channel whose input is a firstorder binary Markov process. Despite the simplicity of the models involved, the characterization of this entropy is a long standing open problem. By ..."
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We study the entropy rate of a binary hidden Markov process (HMP) defined by observing the output of a binary symmetric channel whose input is a firstorder binary Markov process. Despite the simplicity of the models involved, the characterization of this entropy is a long standing open problem
Approximations for the Entropy Rate of a Hidden Markov Process
"... Abstract—Let {Xt} be a stationary finitealphabet Markov chain and {Zt} denote its noisy version when corrupted by a discrete memoryless channel. We present an approach to bounding the entropy rate of {Zt} by the construction and study of a related measurevalued Markov process. To illustrate its ef ..."
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Cited by 3 (0 self)
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Abstract—Let {Xt} be a stationary finitealphabet Markov chain and {Zt} denote its noisy version when corrupted by a discrete memoryless channel. We present an approach to bounding the entropy rate of {Zt} by the construction and study of a related measurevalued Markov process. To illustrate its
Entropy of Hidden Markov Processes and Connections to Dynamical Systems
, 2007
"... 1 Workshop Overview The focus of this workshop was entropy rate of Hidden Markov Processes (HMP)’s, related informationtheoretic quantities and other connections with related subjects. The workshop brought together thirty mathematicians, computer scientists and electrical engineers from institution ..."
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1 Workshop Overview The focus of this workshop was entropy rate of Hidden Markov Processes (HMP)’s, related informationtheoretic quantities and other connections with related subjects. The workshop brought together thirty mathematicians, computer scientists and electrical engineers from
1 Hidden Markov Process: A New Representation, Entropy Rate and Estimation Entropy
, 2006
"... Abstract — We consider a pair of stationary correlated processes {Zn} ∞ n=− ∞ and {Sn} ∞ n=−∞, where the former is observable and the later is hidden. The uncertainty in the estimation of Zn upon its finite past history Z n−1 0 is H(ZnZ n−1 0), and for estimation of Sn upon this observation is H( ..."
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(SnZ n−1 0), which are both sequences of n. The limits of these sequences (and their existence) are of practical and theoretical interest. The first limit is the entropy rate. We call the second limit the estimation entropy. An example of a process jointly correlated to another one is the hidden Markov
Concavity of Mutual Information Rate for InputRestricted FiniteState Memoryless Channels at High SNR
"... We consider a finitestate memoryless channel with i.i.d. channel state and the input Markov process supported on a mixing finitetype constraint. We discuss the asymptotic behavior of entropy rate of the output hidden Markov chain and deduce that the mutual information rate of such a channel is con ..."
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Cited by 4 (4 self)
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We consider a finitestate memoryless channel with i.i.d. channel state and the input Markov process supported on a mixing finitetype constraint. We discuss the asymptotic behavior of entropy rate of the output hidden Markov chain and deduce that the mutual information rate of such a channel
Feedback Capacity of a Class of Symmetric FiniteState Markov Channels
, 2011
"... We consider the feedback capacity of a class of symmetric finitestate Markov channels. Here, symmetry (termed “quasisymmetry”) is defined as a generalized version of the symmetry defined for discrete memoryless channels. The symmetry yields the existence of a hidden Markov noise process that depe ..."
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Cited by 5 (3 self)
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We consider the feedback capacity of a class of symmetric finitestate Markov channels. Here, symmetry (termed “quasisymmetry”) is defined as a generalized version of the symmetry defined for discrete memoryless channels. The symmetry yields the existence of a hidden Markov noise process
1Causal Recursive Parameter Estimation for Discretetime Hidden Bivariate Markov Chains
"... Abstract—An algorithm for causal recursive parameter estimation of a discretetime hidden bivariate Markov chain is developed. In this model, a discretetime bivariate Markov chain is observed through a discretetime memoryless channel. The algorithm relies on the EMbased recursive approach develo ..."
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Abstract—An algorithm for causal recursive parameter estimation of a discretetime hidden bivariate Markov chain is developed. In this model, a discretetime bivariate Markov chain is observed through a discretetime memoryless channel. The algorithm relies on the EMbased recursive approach
Results 1  10
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85