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＜電子ブック＞
Information Theory : Three Theorems by Claude Shannon / by Antoine Chambert-Loir
(La Matematica per il 3+2. ISSN:20385757 ; 144)

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
本文言語	英語
大きさ	XII, 209 p. 1 illus : online resource
著者標目	*Chambert-Loir, Antoine author SpringerLink (Online service)
件　名	LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Coding theory LCSH:Information theory FREE:Mathematics of Computing FREE:Coding and Information Theory
一般注記	Elements of Theory of Probability -- Entropy and Mutual Information -- Coding -- Sampling -- Solutions to Exercises -- Bibliography -- Notation -- Index This book provides an introduction to information theory, focussing on Shannon’s three foundational theorems of 1948–1949. Shannon’s first two theorems, based on the notion of entropy in probability theory, specify the extent to which a message can be compressed for fast transmission and how to erase errors associated with poor transmission. The third theorem, using Fourier theory, ensures that a signal can be reconstructed from a sufficiently fine sampling of it. These three theorems constitute the roadmap of the book. The first chapter studies the entropy of a discrete random variable and related notions. The second chapter, on compression and error correcting, introduces the concept of coding, proves the existence of optimal codes and good codes (Shannon's first theorem), and shows how information can be transmitted in the presence of noise (Shannon's second theorem). The third chapter proves the sampling theorem (Shannon's third theorem) and looks at its connections with other results, such as the Poisson summation formula. Finally, there is a discussion of the uncertainty principle in information theory. Featuring a good supply of exercises (with solutions), and an introductory chapter covering the prerequisites, this text stems out lectures given to mathematics/computer science students at the beginning graduate level HTTP:URL=https://doi.org/10.1007/978-3-031-21561-2

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