Noisy-channel coding theorem: Difference between revisions

Revision as of 23:58, 18 May 2006

Revision as of 00:00, 19 May 2006

Line 86:

*From the joint AEP, we know that the probability that no jointly typical X exists goes to 0 as n grows large. We can bound this error probability by <math>\epsilon</math>.

*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>