Noisy-channel coding theorem: Difference between revisions

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Iseetho (talk | contribs)
Iseetho (talk | contribs)
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*Also from the joint AEP, we know the probability that a particular <math>X_1^n(i)</math> and the <math>Y_1^n</math> resulting from W = 1 are jointly typical is <math>\le 2^{-n(I(X;Y) - 3\epsilon)}</math>. Thus,
 
Define: <math>E_i = \{(X_1^n(i), Y_1^n) \in A_\epsilon^{(n)}\}, i = 1, 2, ..., 2^{nR}</math>
Define
 
<math>E_i = \{(X_1^n(i), Y_1^n) \in A_\epsilon^{(n)}\}, i = 1, 2, ..., 2^{nR}</math>
 
as the event that message i is jointly typical with the sequence received when message 1 is sent.