Noisy-channel coding theorem: Difference between revisions

Revision as of 04:17, 7 October 2023

Revision as of 23:49, 28 October 2023

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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 with 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'tdoes not match the original codeword. This is called ''typical set decoding''.

The probability of error of this scheme is divided into two parts: