000			a
999			_c34020 _d34020
008			250711b xxu||||| |||| 00| 0 eng d
020			_a9783031215605
082			_a004.0151 _bCHA
100			_aChambert-Loir, Antoine
245			_aInformation Theory : Three Theorems by Claude Shannon
260			_bSpringer, _c2022. _aCham :
300			_axii, 209 p. ; _bill., (b & w), _c24 cm.
365			_b64.99 _c€ _d100.40
504			_aIncludes bibliographical Reference Index.
520			_aThis 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.
650			_aCoding
650			_aInformation Theory
650			_aMathematics of Computing
942			_2ddc _cBK