Noisy-channel coding theorem: Difference between revisions

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Iseetho (talk | contribs)
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:::<math>2^{-n(H(X,Y) + \epsilon)} \le p(X_1^n, Y_1^n) \le 2^{-n(H(X,Y) -\epsilon)} \}</math>
 
We say that two sequences <math>X_1^n</math> and <math>Y_1^n</math> are ''jointly typical'' if they lie in the jointly typical set defined above.
 
'''Steps'''
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#The message W is sent across the channel.
#The receiver receives a sequence according to <math>P(y^n|x^n(w))= \prod_{i = 1}^np(y_i|x_i(w))</math>
#Sending these codewords across the channel, we receive <math>Y_1^n</math>, and decode to some source sequence if there exists exactly 1 codeword that is jointly typical inwith Y. If there are no jointly typical codewords, or if there are more than one, an error is declared. An error also occurs if a decoded codeword doesn't match the original codeword. This is called ''typical set decoding''.