Information Theory: Coding Theorems for Discrete Memoryless by Imre Csiszar, Janos Korner

By Imre Csiszar, Janos Korner

Details conception: Coding Theorems for Discrete Memoryless platforms offers mathematical types that contain autonomous random variables with finite diversity. This three-chapter textual content in particular describes the attribute phenomena of knowledge idea.

Chapter 1 bargains with details measures in uncomplicated coding difficulties, with emphasis on a few formal houses of Shannon’s info and the non-block resource coding. bankruptcy 2 describes the houses and sensible features of the two-terminal structures. This bankruptcy additionally examines the noisy channel coding challenge, the computation of channel potential, and the arbitrarily various channels. bankruptcy three seems to be into the speculation and practicality of multi-terminal systems.

This publication is meant essentially for graduate scholars and learn staff in arithmetic, electric engineering, and desktop technological know-how.

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Extra info for Information Theory: Coding Theorems for Discrete Memoryless Systems. Probability and Mathematical Statistics. A Series of Monographs and Textbooks

Sample text

Using them, one can transform linear equations for information measures resp. their analogues for set functions into linear equations involving solely unconditional entropies resp. set-function analogues of the latter. Thus it suffices to prove the assertion for such equations. To this end, we shall show that a linear expression of form Or XQM(UA,) Σ'ΜΧάεσ) a a ie σ with σ ranging over the subsets of (1, 2, . . , k) vanishes identically iff all coefficients ca are 0. Both statements are proved in the same way, hence we give the proof only for entropies.

3 and it implies the last one again by averaging. _,) / = l k /<*, Xk*Y)=ltI(XiAY\Xl i= 1 *,·_,); similar identities hold for conditional entropy and conditional mutual information. 4 completely conforms with the intuitive interpretation of information measures. , the identity I(XJAZ) = I(X AZ) + I{YAZ\X) means that the information contained in (X, Y) about Z consists of the information provided by X about Z plus the information Y provides about Z in the knowledge of X. 2 give rise to a number of inequalities with equally obvious intuitive meaning.

First, for a DMS with generic distribution P it gives the precise asymptotics—in the nk exponential sense—of the probability of error of the best codes with — -► R (of course, the result is trivial when R ^ H(P)). Second, it shows that this optimal performance can be achieved by codes not depending on the generic distribution of the source. 1, namely that for — -* R

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