1. Fano's inequality
Intuition: If Y is a function of X, Y = g(X), then H(Y|X) =0 . If we can only estimate Y from X with some probability of error P(e), we can image that H(Y|X) will be small if P(e) is small ,and H(Y|X)->0 , as P(e) -> 0.
Proof: we model the process as a Markov Chain
X------> Y--------> \hat{X}
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