Explicit Causal Recursive Estimators for Continuous-Time Bivariate Markov Chains

Mark, Brian L.; Ephraim, Yariv

doi:10.1109/tsp.2014.2314434

Cited by 12 publications

(14 citation statements)

References 39 publications

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“…with explicit forms being shown in Eq. (7). Intuitively, if the two subsystems do not interact with each other efficiently (I(X, S) = 0) then we must have both I B (X, S) = 0 and I D (X, S) = 0.…”

Section: Interactions Between Non-markovian Systemsmentioning

confidence: 99%

“…Usually, the dynamics of interacting systems in random environments with time-invariant parameters (temperatures, chemical potentials, etc.) and infinite degrees of freedom is always considered to be non-Markovian with finite memories [7]. Although the usual analytical and numerical methods for Markov processes can be also applied for getting the pictures of both stochastic dynamics and thermodynamics of a composite Markov system, it has been proven to be difficult that we can depict the behaviours of the subsystems with the same ingredient.…”

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confidence: 99%

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Non-Markovian nonequilibrium information dynamics

Zeng

Jin

2018

Phys. Rev. E

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We probe into the dynamics of interacting non-Markovian information systems. The stochastic dynamics of information has two aspects: the self-evolution and interaction. We show that self-evolution of a non-Markovian information system can be described by a Markov-type master equation with memory dependence. We also reveal that the interaction between systems can be fully embodied into the information dynamics of the composite information system. To characterize time-irreversibility of the self-evolution and the interaction, we apply the landscape-flux theory to both stochastic and thermal information dynamics.The driving force of the nonequilibrium information dynamics can be decomposed into time-reversible (detailed balance preserving landscape part) and -irreversible (detailed balance breaking nonequilibrium flux part) parts. The time-irreversible part of the driving force fully depicts the time-irreversibility behavior in the stochastic dynamics. The time-irreversibility of the interactions between systems reflected in nonequilibrium thermodynamics can be seen in the decomposition of the mutual information rate which corresponds to decomposition of the driving force. In particularly, the time-irreversible part of mutual information rate reveals the underlying relationship among the entropy production rates of the information systems. We propose the finite memory approximation method and demonstrate that the above mentioned features can be found in a wide class of non-Markovian nonequilibrium information systems. Finally, we derive the lower and upper bounds for informational entities under concern with clearly meanings.Studies on the nonequilibrium behaviors of two interacting systems with finite states have shown their importance in meso-and microscopic information dynamics [1][2][3][4][5][6]. Usually, the dynamics of interacting systems in random environments with time-invariant parameters (temperatures, chemical potentials, etc.) and infinite degrees of freedom is always considered to be non-Markovian with finite memories [7]. Although the usual analytical and numerical methods for Markov processes can be also applied for getting the pictures of both stochastic dynamics and thermodynamics of a composite Markov system, it has been proven to be difficult that we can depict the behaviours of the subsystems with the same ingredient. This is because the two subsystems may also be random environments with time-variant parameters for each other due to the comparable sizes and state-switching rates of the subsystems. This indicates that none of the subsystems needs to be Markovian. Because of the existence of the interactions, every subsystem has to adjust itself to adapt to the time-variant environment (the other subsystem) and then the corresponding process shows a remarkable path-dependence by summing away the degree of freedom of the other subsystem, which means it has a memory. The Information of the past states in a memory are always embedded into the parameters of the dynamics of the system to determine the ...

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Section: Interactions Between Non-markovian Systemsmentioning

confidence: 99%

mentioning

confidence: 99%

Non-Markovian nonequilibrium information dynamics

Zeng

Jin

2018

Phys. Rev. E

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“…Let denote a 1 column vector with a one in the position and zeros elsewhere. Then, (29) where denotes matrix transpose. Dividing both sides of (29) by , and using (19), we obtain,…”

Section: A Initial Distributionmentioning

confidence: 99%

Causal Recursive Parameter Estimation for Discrete-Time Hidden Bivariate Markov Chains

Ephraim

Mark

2015

IEEE Trans. Signal Process.

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An algorithm for causal recursive parameter estimation of a discrete-time hidden bivariate Markov chain is developed. In this model, a discrete-time bivariate Markov chain is observed through a discrete-time memoryless channel. The algorithm relies on the EM-based recursive approach developed by Stiller and Radons for hidden Markov models. A distinct advantage of the discrete-time hidden bivariate Markov chain model is that the sojourn time distribution of its observable process in each state is phase-type rather than geometric as in the hidden Markov model. Phase-type distributions can approximate any desired sojourn time distribution. Particular phase-type distributions include mixtures and convolutions of geometric distributions. The parameter estimation algorithm requires causal recursive estimation of the relevant statistics in each EM step. These statistics include the number of jumps of the bivariate Markov chain from one state to another, including self transitions, in the given observation interval, and first-and second-order statistical averages of the observable process in each state when the memoryless channel is Gaussian. We develop the explicit recursions and demonstrate the performance of the algorithm in estimating the model's parameter and its sojourn time distribution in a numerical example.

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“…A wide range of multimedia traffic can be represented with an MMPP model, which is accurate and reasonable [19], and the Poisson arrival is the special case of this model. Amounts of multimedia services are existing in the present and future wireless networks, which can be categorized into heterogeneous classes with different delay demands.…”

Section: A Traffic and Queuing Modelsmentioning

confidence: 99%

“…If the Markov chain {(F t , S t , C t )} is not assumed to be irreducible, there can be more than one solution for (19). The solution π is the left eigenvector of P corresponding to the eigenvalue 1.…”

Section: Cross-layer Queuing and Delay Analysismentioning

confidence: 99%

Delay-Aware Energy-Efficient Communications Over Nakagami- <inline-formula> <tex-math notation="LaTeX">$m$</tex-math></inline-formula> Fading Channel With MMPP Traffic

Wang

Tao

Chen

et al. 2015

IEEE Trans. Commun.

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In this paper, we propose a cross-layer design framework for transmitting Markov modulated Poisson process (MMPP) traffic over Nakagami-m fading channel with delay demands. The adaptive modulation and coding (AMC) technique is used at the physical layer. The energy efficiency is described as the average throughput over the average transmission power, where both of throughput and transmit power have full consideration of the queuing system. We first derive the closed-form expressions of the delay and the energy efficiency with the stationary distribution of the system. We then derive the energy efficient thresholds to choose the AMC transmission modes. At last, we derive the transmission policy to maximize the energy efficiency with delay constraints. Numerical results are provided to support the theoretical development.Index Terms-Cross-layer design, energy efficiency, adaptive modulation and coding, queuing theory, finite state Markov channel, Markov modulated Poisson process, delay.

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Explicit Causal Recursive Estimators for Continuous-Time Bivariate Markov Chains

Cited by 12 publications

References 39 publications

Non-Markovian nonequilibrium information dynamics

Non-Markovian nonequilibrium information dynamics

Causal Recursive Parameter Estimation for Discrete-Time Hidden Bivariate Markov Chains

Delay-Aware Energy-Efficient Communications Over Nakagami- <inline-formula> <tex-math notation="LaTeX">$m$</tex-math></inline-formula> Fading Channel With MMPP Traffic

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