Designed for advanced undergraduate or graduate courses in communications in electrical engineering departments, this book presents a mathematical description of the essential areas that define the field of communication. Among the topics covered are: signal theory and signals in linear vector spaces; noise and its effects; information theory and coding; representation of information; statistical detection theory; communication performance in AWGN; error-control coding; rate-distortion theory and achieving real-world performance; the algebraic structure of communication signals in Hilbert space and over Galois fields; the role and contribution of signal space metrics to communication performance; the distinction between the performance-related algebraic structure of codes and alogorithmics details; and rate-distortion theory and its use in balancing trade-offs.
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