Lecture 8: Noisy Channel Coding (III): The Noisy-Channel Coding Theorem

author: David MacKay, University of Cambridge
produced by: David MacKay (University of Cambridge)
author: David MacKay, University of Cambridge
published: Nov. 5, 2012,   recorded: May 2012,   views: 1311
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Reviews and comments:

Comment1 Ethan, November 11, 2015 at 11:39 p.m.:

I'm having a problem with the very end of the proof. P2 vanishes if M>>NH2(f); doesn't this mean that R<<C? If the rate has to be much less than the capacity, then how have we proved the theorem, which allows us to construct codes with rates arbitrarily close to C with vanishingly small error?


Comment2 ergodic, November 27, 2016 at 1:14 a.m.:

To Ethan: the rate is K/N = 1 - M/N. In order to make the error as small as desired we would increase M. But we are also free to increase N (increase the number of times the channel is used) to keep the rate away from zero -- but we won't be able to exceed C.

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