I'm trying to go through Shannon's paper "A Mathematical Theory of Communication" to improve my understanding of information theory.(adsbygoogle = window.adsbygoogle || []).push({});

In Part I (Discrete Noiseless Systems) Shannon states:

Suppose all sequences of the symbols S_{1}, . . . ,S_{n}are allowed and these symbols have durations t_{1}, . . . ,t_{n}. What is the channel capacity?

If N(t) represents the number of sequences of duration t we have

N(t) = N(t -t_{1})+N(t -t_{2})+...+N(t -t_{n}):

The total number is equal to the sum of the numbers of sequences ending in S_{1}, S_{2}, . . . , S_{n}and these are N(t -t_{1}), N(t -t_{2}), . . . ,N(t -t_{n}), respectively.

So I can't understand how this sum is actually working. For example, if t_{1}=2s and t_{2}=4s, then the first term in the sum is the number of all sequences ending in S_{1}as expected. However the second term is going to be the number of all sequences ending ineitherS_{1},S_{1}or S_{2}. So this means that some of the sequences ending in S_{1}have been counted twice by this sum.

Am I missing something here? Or am I correct and the right hand side of the equation is going to be larger than the left?

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# Question about Shannon's mathematics

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