Evgueni A. Haroutunian, Mariam E. Haroutunian and Ashot N. Harutyunyan (2008), "Reliability Criteria in Information Theory and in Statistical Hypothesis Testing", Foundations and Trends® in Communications and Information Theory: Vol. 4: No. 2–3, pp 97-263. http://dx.doi.org/10.1561/0100000008

© 2008 E. A. Haroutunian, M. E. Haroutunian and A. N. Harutyunyan

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**In this article:**

1. Introduction

2. E-capacity of the Discrete Memoryless Channel

3. Multiuser Channels

4. E-capacity of Varying Channels

5. Source Coding Rates Subject to Fidelity and Reliability Criteria

6. Reliability Criterion in Multiterminal Source Coding

7. Logarithmically Asymptotically Optimal Testing of Statistical Hypotheses

Basic Notations and Abbreviations

References

This survey is devoted to one of the central problems of Information Theory — the problem of determination of interdependence between coding rate and error probability exponent for different information transmission systems. The overview deals with memoryless systems of finite alphabet setting. It presents material complementary to the contents of the series of the most remarkable in Information Theory books of Feinstain, Fano, Wolfowitz, Gallager, Csiszar and Körner, Kolesnik and Poltirev, Blahut, Cover and Thomas and of the papers by Dobrushin, Gelfand and Prelov.

We briefly formulate fundamental notions and results of Shannon theory on reliable transmission via coding and give a survey of results obtained in last two-three decades by the authors, their colleagues and some other researchers. The paper is written with the goal to make accessible to a broader circle of readers the theory of rate-reliability. We regard this concept useful to promote the noted problem solution in parallel with elaboration of the notion of reliability-reliability dependence relative to the statistical hypothesis testing and identification.

1. Introduction

2. E-capacity of the DMC

3. Multiuser Channels

4. E-capacity of Varying Channels

5. Source Coding Rates Subject to Fidelity and Reliability Criteria

6. Reliability Criterion in Multiterminal Source Coding

7. Logarithmically Asymptotically Optimal Testing of Statistical Hypotheses

Basic Notations and Abbreviations

References

*Reliability Criteria in Information Theory and Statistical Hypothesis Testing* is devoted to one of the central problems of
Information Theory; the problem of determination of interdependence of coding rate and of error probability exponent for different information
transmission systems. The overview deals with memoryless systems of finite alphabet setting.

*Reliability Criteria in Information Theory and Statistical Hypothesis Testing*briefly formulates fundamental notions and
results of Shannon theory on reliable transmission via coding and gives a survey of results obtained in last two-three decades by the authors,
their colleagues and other researchers. The book is written with the goal to make accessible to a broader circle of readers the concept of
rate-reliability. This concept is useful to solve these problems as well as elaborating the idea of reliability-reliability dependence related
to statistical hypothesis testing and identification.

*Reliability Criteria in Information Theory and Statistical Hypothesis Testing* is for students, researchers and
professionals working in Information Theory.