Information Theory

Basic Concepts in Information Theory and Coding: The by Solomon W. Golomb

By Solomon W. Golomb

Basic recommendations in details idea and Coding is an outgrowth of a one­ semester introductory direction that has been taught on the college of Southern California because the mid-1960s. Lecture notes from that path have advanced in keeping with pupil response, new technological and theoretical enhance­ ments, and the insights of college contributors who've taught the path (in­ cluding the 3 of us). In offering this fabric, we've made it available to a wide viewers through proscribing necessities to uncomplicated calculus and the ele­ mentary thoughts of discrete chance conception. to maintain the fabric compatible for a one-semester direction, we've got restricted its scope to discrete details conception and a common dialogue of coding idea with out special remedy of algorithms for encoding and deciphering for numerous particular code sessions. Readers will locate that this publication deals an surprisingly thorough remedy of noiseless self-synchronizing codes, in addition to the good thing about challenge sections which have been honed by way of reactions and interactions of numerous gen­ erations of vibrant scholars, whereas Agent 00111 presents a context for the dialogue of summary concepts.

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35 Introduction Roughly speaking, transition lines in a state diagram indicate the direction of flow of probability between states as the index i increases; arrows in the equivalent cluster diagram indicate this same effect. , those clusters having no exiting transitions to other clusters in the diagram. When used to model languagelike information sources, Markov chains generally consist of a single (terminal) cluster. If there were two terminal clusters, a transition into one terminal cluster would forever prevent the occurrence of state sequences within a different cluster.

For this purpose, a secondorder Markov source based on the transition probabilities of the language should prove adequate for testing. However, a memoryless source could not possibly provide the digraph and trigraph statistics to imitate the language properly. 1 showed that approximately 2nH(M IMOO) typical sequences of length n occur in a Markov source having entropy H(M IMOO) bits/symbol. This information is useful in determining the number of distinct n-tuples in the language that an n-tuple processor must be prepared to handle.

3. A spy is employed as a newscaster for a radio station to which his confederate listens. " He sends the contactme message with probability p. The method of communication is as follows: If the newscaster wishes to broadcast contact me, he reports all news from the Associated Press wire, a source of entropy H(AP) bits per broadcast. ) bits per broadcast. The news source used is obvious to the listener. (a) What is the a priori uncertainty about the newscast? Interpret your answer. (b) What is the mutual information between the spy's contact-me, donot-contact-me alphabet and the newscast?

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