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This book deals with certain important problems in Classical and Quantum Information Theory which is basically a subject involving the proof of coding theorems for data compression and the efficient transmission of information over noisy channels. By coding theorems, we mean proving the existence of codes that would achieve maximum possible data compression without distortion or with an admissible degree of distortion or would enable us to transmit data over a noisy channel so that the input message can be retrieved from the output to an arbitrary degree of accuracy (ie with arbitrarily small error probability) when the input data strings that are coded are made sufficiently long. In classical information theory, the important problems discussed in this book are as follows. First, the construction of no-prefix and uniquely decipherable codes from a probabilistic source and properties of the minimum average length of such codes with relation to the entropy of the source. Second, the proof the specific form of the Shannon entropy function based on fundamental properties that the entropy function of a source should possess like the conditional additivity of the joint entropy of two dependent sources, monotone increasing property of the entropy as a function of the number of alphabets in the source under a uniform distribution and continuity of the entropy as a function of the source probability distribution. For estabilishing properties of the minimum average code length, we require the Kraft inequality regarding the codeword lengths.
The Kraft inequality is a relationship between the lengths of the codewords of the different source symbols and the size of the encoding alphabet. The validity of this inequality implies the existence of a no prefix code with the specified codeword lengths, the no prefix property of a code implies unique decipherability which in turn implies the validity of Kraft’s inequality.
Quantum Information Theory, A Selection of Matrix Inequalities
Stochastic Filtering Theory Applied to Electromagnetic Fields and Strings
Wigner-distributions in Quantum Mechanics
Quantization of Classical Field Theories
Statistical Signal Processing
Quantum Field Theory, Quantum Statistics, Gravity, Stochastic Fields and Information Problems in Information Theory
It will be very helpful for students of Undergraduate and Postgraduate Courses in Electronics, Communication and Signal Processing