Transcription of INTRODUCTION TO INFORMATION THEORY
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INTRODUCTION TO INFORMATION THEORY
1 INTRODUCTION TO INFORMATION THEORY {ch:intro_info}This chapter introduces some of the basic concepts of INFORMATION THEORY , as wellas the definitions and notations of probabilities that will be used throughoutthe book. The notion of entropy, which is fundamental to the whole topic ofthis book, is introduced here. We also present the main questions of informationtheory, data compression and error correction, and state Shannon s Random variablesThe main object of this book will be the behavior of large sets ofdiscreterandom variables. A discrete random variableXis completely defined1bythe set of values it can take,X, which we assume to be a finite set, and itsprobability distribution{pX(x)}x X.
measure for an ‘infinitesimal element’ dxwill be denoted by dpX(x). Each time pX admits a density (with respect to the Lebesgue measure), we shall use the notation pX(x) for the value of this density at the point x. The total probability P(X∈ A) that the variable Xtakes value in some (Borel) set A ⊆ X is given by the integral:
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