A theorem on the entropy of certain binary sequences and applications--I
Wyner, A.; Ziv, J.
Information Theory, IEEE Transactions on
Volume 19, Issue 6, Nov 1973 Page(s): 769 - 772
Digital Object Identifier  
Summary: In this, the first part of a two-part paper, we establish a theorem concerning the entropy of a certain sequence of binary random variables. In the sequel we will apply this result to the solution of three problems in multi-user communication, two of which have been open for some time. Specifically we show the following. LetXandYbe binary randomn-vectors, which are the input and output, respectively, of a binary symmetric channel with "crossover" probabilityp_0. LetH{X}andH{ Y}be the entropies ofXandY, respectively. Then begin{equation} begin{split} frac{1}{n} H{X} geq h(alpha_0), qquad 0 leq alpha_0 &leq 1, Rightarrow \ qquad qquad &qquad frac{1}{n}H{Y} geq h(alpha_0(1 - p_0) + (1 - alpha_0)p_0) end{split} end{equation} whereh(lambda) = -lambda log lambda - (1 - lambda) log(l - lambda), 0 leq lambda leq 1.

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