Noisy-channel coding theorem: Difference between revisions

Revision as of 21:53, 18 May 2006

Revision as of 21:57, 18 May 2006

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By an AEP-related argument, given a channel, length n strings of source symbols <math>X_1^{n}</math>, and length n strings of channel outputs <math>Y_1^{n}</math>, we can define a jointly typical set by the following:

<math>A_\epsilon^{(n)} = \{(x^n, 2y^{-n(H(X)+ \epsilon)}in \lemathcal p(X_1X^n) \letimes 2\mathcal Y^{-n(H(X) - \epsilon)}</math>

:::<math>2^{-n(H(X)+\epsilon)} \le p(X_1^n) \le 2^{-n(H(X) - \epsilon)}</math>

:::<math>2^{-n(H(Y) + \epsilon)} \le p(Y_1^n) \le 2^{-n(H(Y)-\epsilon)}</math>