Asymptotically Optimal Tests for Finite Markov Chains

Boza, L.

doi:10.1214/aoms/1177693067

Cited by 35 publications

(32 citation statements)

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“…To any ergodic FSMC we associate the mutual information cost function (5) and define its capacity as (6) In the definitions (5) and (6), the terms and , respectively, denote the mutual information between and the pair when , and the conditional mutual information (see [8]) between and the pair given , where is an -valued random variable (r.v.) whose marginal distribution is given by the stationary measure , is an -valued r.v.…”

Section: B Capacity Of Ergodic Fsmcsmentioning

confidence: 99%

“…Using known results on binary hypothesis tests for irreducible Markov chains (see [5], [24] and [10, pp. 72-82]) it is possible to show that a decoder can be chosen in such a way that, asymptotically in , its typeerror probability achieves the exponent (recall (15)) while its type-error probability is vanishing.…”

Section: Binary Hypothesis Test For the Confirmation Phasementioning

confidence: 99%

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The Error Exponent of Variable-Length Codes Over Markov Channels With Feedback

Como

Yüksel

Tatikonda

2009

IEEE Trans. Inform. Theory

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Abstract-The error exponent of Markov channels with feedback is studied in the variable-length block-coding setting. Burnashev's classic result is extended to finite-state ergodic Markov channels. For these channels, a single-letter characterization of the reliability function is presented, under the assumption of full causal output feedback, and full causal observation of the channel state both at the transmitter and at the receiver side. Tools from stochastic control theory are used in order to treat channels with intersymbol interference (ISI). Specifically, the convex-analytic approach to Markov decision processes is adopted in order to handle problems with stopping time horizons induced by variable-length coding schemes.Index Terms-Channel coding with feedback, error exponents, finite-state Markov channels, Markov decision processes, variablelength block codes.

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Section: B Capacity Of Ergodic Fsmcsmentioning

confidence: 99%

Section: Binary Hypothesis Test For the Confirmation Phasementioning

confidence: 99%

The Error Exponent of Variable-Length Codes Over Markov Channels With Feedback

Como

Yüksel

Tatikonda

2009

IEEE Trans. Inform. Theory

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“…Boza [14], Davisson, Longo, Sgarro [15], Natarajan [16], Csiszár, Cover, Choi [17], and Csiszár [18]. (Throughout this paper, the base of the logarithm is |Σ|.…”

Section: B Markov Typementioning

confidence: 99%

On the VC-dimension of binary codes

Weinberger

Shayevitz

2017

2017 IEEE International Symposium on Information Theory (ISIT)

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Abstract-We investigate the asymptotic rates of length-n binary codes with VC-dimension at most dn and minimum distance at least δn. Two upper bounds are obtained, one as a simple corollary of a result by Haussler and the other via a shortening approach combining Sauer-Shelah lemma and the linear programming bound. Two lower bounds are given using Gilbert-Varshamov type arguments over constant-weight and Markov-type sets.

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“…In [30] error exponent is computed for testing between two different Markov sources (without additive noise in the observations); for applications and extensions of this result in Markov source-coding see [31], [32], [33], [34]. Error exponents for HMMs are considered in [23] and [24], as detailed above.…”

Section: Introductionmentioning

confidence: 99%

Optimal Detection and Error Exponents for Hidden Semi-Markov Models

Bajović

Stanković

et al. 2018

IEEE J. Sel. Top. Signal Process.

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Abstract. We study detection of random signals corrupted by noise that over time switch their values (states) between a finite set of possible values, where the switchings occur at unknown points in time. We model such signals as hidden semi-Markov signals (HSMS), which generalize classical Markov chains by introducing explicit (possibly non-geometric) distribution for the time spent in each state. Assuming two possible signal states and Gaussian noise, we derive optimal likelihood ratio test and show that it has a computationally tractable form of a matrix product, with the number of matrices involved in the product being the number of process observations. The product matrices are independent and identically distributed, constructed by a simple measurement modulation of the sparse semi-Markov model transition matrix that we define in the paper. Using this result, we show that the Neyman-Pearson error exponent is equal to the top Lyapunov exponent for the corresponding random matrices. Using theory of large deviations, we derive a lower bound on the error exponent. Finally, we show that this bound is tight by means of numerical simulations.

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Asymptotically Optimal Tests for Finite Markov Chains

Cited by 35 publications

References 0 publications

The Error Exponent of Variable-Length Codes Over Markov Channels With Feedback

The Error Exponent of Variable-Length Codes Over Markov Channels With Feedback

On the VC-dimension of binary codes

Optimal Detection and Error Exponents for Hidden Semi-Markov Models

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