Error-Exponent of Distributed Hypothesis Testing for Gilbert-Elliot Source Models
Adamou, Ismaila Salihou; Dupraz, Elsa; Zribi, Amin; Matsumoto, Tad (2023-10-10)
IEEE
10.10.2023
I. S. Adamou, E. Dupraz, A. Zribi and T. Matsumoto, "Error-Exponent of Distributed Hypothesis Testing for Gilbert-Elliot Source Models," 2023 12th International Symposium on Topics in Coding (ISTC), Brest, France, 2023, pp. 1-5, doi: 10.1109/ISTC57237.2023.10273559.
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© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
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Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202403252422
https://urn.fi/URN:NBN:fi:oulu-202403252422
Tiivistelmä
Abstract
This paper considers Distributed Hypothesis Testing (DHT), in which a source X is encoded given that a side information Y is available only to the decoder. The decoder’s task is to make a decision between two hypothesis H0 and H1 related to the joint probability distribution of X and Y. While most works on DHT have adopted an information-theoretic approach by providing generic error exponents for the decision error, we focus on a specific and practical source model: the Gilbert-Elliot (GE) model. The later is a two-states hidden Markov model which describes time-varying correlation between X and Y. Starting from the generic error exponents, we develop a method for numerically estimating the error exponent for the GE model. We provide numerical results to evaluate the impact of the model parameters on the error exponents and explore the tradeoff between two types of error events, namely the testing error and the binning error.
This paper considers Distributed Hypothesis Testing (DHT), in which a source X is encoded given that a side information Y is available only to the decoder. The decoder’s task is to make a decision between two hypothesis H0 and H1 related to the joint probability distribution of X and Y. While most works on DHT have adopted an information-theoretic approach by providing generic error exponents for the decision error, we focus on a specific and practical source model: the Gilbert-Elliot (GE) model. The later is a two-states hidden Markov model which describes time-varying correlation between X and Y. Starting from the generic error exponents, we develop a method for numerically estimating the error exponent for the GE model. We provide numerical results to evaluate the impact of the model parameters on the error exponents and explore the tradeoff between two types of error events, namely the testing error and the binning error.
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