مرکز منطقه ای اطلاع رساني علوم و فناوري - Sequences achieving the boundary of the entropy region for a two-source are virtually memoryless (Corresp.)

DocumentCode :

942880

Title :

Sequences achieving the boundary of the entropy region for a two-source are virtually memoryless (Corresp.)

Author :

Marton, Katalin

Volume :

Issue :

fYear :

1987

fDate :

5/1/1987 12:00:00 AM

Firstpage :

443

Lastpage :

448

Abstract :

For a joint distribution ${\\rm dist}(X,Y)$ , the function $T(t)=\\min { H(Y|U): I(U \\wedge Y|X)=O, H(X|U)\\geq t}$ is an important characteristic. It equals the asymptotic minimum of $(1/n)H(Y^{n})$ for random pairs of sequences $(X^{n}, Y^{n})$ , where $frac{1}{n} \\sum ^{n}_{i=1}{\\rm dist} X_{i} \\sim {\\rm dist} X, {\\rm dist} Y^{n}|X^{n} = ({\\rm dist} Y|X)^{n}, frac{1}{n}H(X^{n})\\geq t.$ We show that if, for $(X^{n}, Y^{n})$ as given, the rate pair $[(1/n)H(X^{n})$ , $(1/n)H(Y^{n})]$ approaches the nonlinear part of the curve $(t,T(t))$ , then the sequence $X^{n}$ is virtually memoryless. Using this, we determine some extremal sections of the rate region of entropy characterization problems and find a nontrivial invariant for weak asymptotic isomorphy of discrete memoryless correlated sources.