A Toolbox for Refined Information-Theoretic Analyses with Applications
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929369915588608 |
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| author | Merhav, Neri Weinberger, Nir |
| author_facet | Merhav, Neri Weinberger, Nir |
| contents | This monograph offers a toolbox of mathematical techniques, which have been effective and widely applicable in information-theoretic analysis. The first tool is a generalization of the method of types to Gaussian settings, and then to general exponential families. The second tool is Laplace and saddle-point integration, which allow to refine the results of the method of types, and are capable of obtaining more precise results. The third is the type class enumeration method, a principled method to evaluate the exact random-coding exponent of coded systems, which results in the best known exponent in various problem settings. The fourth subset of tools aimed at evaluating the expectation of non-linear functions of random variables, either via integral representations, or by a refinement of Jensen's inequality via change-of-measure, by complementing Jensen's inequality with a reversed inequality, or by a class of generalized Jensen's inequalities that are applicable for functions beyond convex/concave. Various application examples of all these tools are provided along this monograph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00744 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Toolbox for Refined Information-Theoretic Analyses with Applications Merhav, Neri Weinberger, Nir Information Theory This monograph offers a toolbox of mathematical techniques, which have been effective and widely applicable in information-theoretic analysis. The first tool is a generalization of the method of types to Gaussian settings, and then to general exponential families. The second tool is Laplace and saddle-point integration, which allow to refine the results of the method of types, and are capable of obtaining more precise results. The third is the type class enumeration method, a principled method to evaluate the exact random-coding exponent of coded systems, which results in the best known exponent in various problem settings. The fourth subset of tools aimed at evaluating the expectation of non-linear functions of random variables, either via integral representations, or by a refinement of Jensen's inequality via change-of-measure, by complementing Jensen's inequality with a reversed inequality, or by a class of generalized Jensen's inequalities that are applicable for functions beyond convex/concave. Various application examples of all these tools are provided along this monograph. |
| title | A Toolbox for Refined Information-Theoretic Analyses with Applications |
| topic | Information Theory |
| url | https://arxiv.org/abs/2406.00744 |