A Toolbox for Refined Information-Theoretic Analyses with Applications
<|reference_start|>A Toolbox for Refined Information-Theoretic Analyses with Applications: 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.<|reference_end|>
@article{merhav2024a,
    title={A Toolbox for Refined Information-Theoretic Analyses with Applications},
    author={Neri Merhav and Nir Weinberger},
    journal={arXiv preprint arXiv:2406.00744},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.00744},
    primaryClass={cs.IT math.IT}
}