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A simple proof of the Ahlswede - Csiszár one-bit theorem (Corresp.)

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It is proved that if (X,Y) are two finite alphabet correlated sources with p(x,y)> 0 for all (x,y) \in ({cal X} \times {cal Y}) , and if a function F(X,Y) is \alpha -sensitive, then the rate R of transmission from X to Y necessary to compute F(X,Y) reliably must be greater than H(X|Y) . The same result holds if the function is highly sensitive and for every x_{1} \neq x_{2} \in {cal X} , then the number of elements y \in {cal Y} with p(x_{l},y) \cdot p(x_{2}, y)> 0 is different from one.

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Information Theory, IEEE Transactions on  (Volume:29 ,  Issue: 6 )