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I'm confused by what it means when it says rate. At the bottom of page 15 and page 16 here http://www0.maths.ox.ac.uk/system/files/coursematerial/2014/3093/6/Lecture_notes.pdf it seems to be saying that the rate is the same as the entropy of the source. Shouldn't it instead say that we need $H/(log_2k)$ to be less than the channel capacity, where each source symbol $x\in A$ is coded by $c:\ A\to\ B^k$ as $c(x)$ which has length k?

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Entropy $H$ as stated is per source symbol. A source output of $n$ symbols has entropy $nH$. Note that the Theorem on p. 15 states that you're encoding a message of length $n.$

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  • $\begingroup$ Shouldn't each output $b \in B^k$ have the same entropy as one symbol in $A$ though (if $c$ is uniquely decipherable)? Why would encoding one symbol as a word of length k increase the entropy? $\endgroup$
    – user152440
    May 14 '15 at 12:32
  • $\begingroup$ See edited answer $\endgroup$
    – kodlu
    May 14 '15 at 14:03

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