Theory of Information and its Value

• Foreword.- Preface.- 1 Definition of information and entropy in the absence of noise- 2 Encoding of discrete information in the absence of noise and penalties.- 3 Encoding in the presence of penalties. The first variational problem- 4 The first asymptotic theorem and relative results.- 5 Computation of entropy for special cases. Entropy of stochastic processes.- 6 Information in the presence of noise. The Shannon's amount of information.- 7 Message transmission in the presence of noise. The second asymptotic theorem and its various formulations.- 8 Channel capacity. Important particular cases of channels.- 9 Definition of the value of information.- 10 The value of Shannon information for the most important Bayesian systems.- 11 Asymptotical results related to the value of information. The Third asymptotic theorem.- 12 Information theory and the second law of thermodynamics.- Appendix Some matrix (operator) identities.- Index.

“The book could be useful in advanced graduate courses with students, who are not afraid of integrals and probabilities.” (Jaak Henno, zbMATH 1454.94002, 2021)