Large deviations, hypotheses testing, and source coding for finite Markov chains

Natarajan, S.

doi:10.1109/tit.1985.1057036

Cited by 72 publications

(75 citation statements)

References 7 publications

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“…In the book of Csiszár and Shields [5] different asymptotic aspects of two hypotheses testing for independent identically distributed observations are considered via theory of large deviations. Similar problems for Markov dependence of experiments were investigated by Natarajan [13], Haroutunian [7], [8], Haroutunian and Navaei [9] and others.…”

Section: Introductionmentioning

confidence: 74%

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On error probability exponents of many hypotheses optimal testing illustrations

Navaei¹

2011

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Abstract. In this paper we study a model of hypotheses testing consisting of with to simple homogeneous stationary Markov chains ith finite number of states such that having different distributions from four possible transmission probabilities.For solving this problem we apply the method of type and large deviation techniques (LTD). The case of two objects having different distributions from to given probability distribution as examined by Ahlswedeh and Haroutunian.Résumé. Dans cet article nousétudions un modèle de tests d'hypothèses composé de deux chaines de Markov stationnaires homogènes et simples avec un nombre fini d'états ayant différentes distributions parmi quatre probabilités de transition possibles. Pour résoudre ce problème, nous appliquons la méthode des types et des techniques de grandes deviations. Le cas de deux objets ayant différentes distributions issues d'une distribution de probabilité donnée, aété examiné par Ahlswedeh et Haroutunian.

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Section: Introductionmentioning

confidence: 74%

“…The problem of many (L > 2) hypotheses testing on distributions of independent observations is studied in [13], [11] via large deviations techniques.…”

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confidence: 99%

On error probability exponents of many hypotheses optimal testing illustrations

Navaei¹

2011

afst

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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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“…Based on the NP lemma [1, pp. [22][23][24][25][26][27][28][29], it can be shown that the solution of (15) is in the form of a likelihood ratio test (LRT); that is, 3 (16) where 0 and 0 (x) 1 are such that max …”

Section: A Characterization Of Optimal Decision Rulementioning

confidence: 99%

“…On the other hand, no prior information is assumed in the minimax approach, and a minimax decision rule minimizes the maximum of risk functions defined over the parameter space [1, pp. [13][14][15][16][17][18][19][20][21][22], [4]. The Bayesian and minimax frameworks can be considered as two extreme cases of prior information.…”

Section: Introductionmentioning

confidence: 99%