I am trying to work out this problem:

Assume that we are transmitting data from a dictionary of 15 symbols. Let the probability of sending one symbol be the same as that of sending any other symbol. Calculate how often we need to fetch a symbol to transmit information at a rate of 5 bits/s.

How can this be found?

  • $\begingroup$ It would be nice if you write also what you may have thought or tried to do. $\endgroup$ May 7, 2014 at 20:02
  • $\begingroup$ I am starting to learn about entropy, all I basically know is the formula of entropy which in this case I think is not applicable since the probabilities are not given $\endgroup$ May 7, 2014 at 20:22
  • $\begingroup$ @user1930901: 15 equally likely symbols means each symbol has a probability of $1/15$. See my answer for a hint. $\endgroup$
    – Matt L.
    May 7, 2014 at 20:23

1 Answer 1


HINT: Compute the entropy $H$ of your source and note that in your case it represents the number of bits required to represent each symbol. Then from

$\quad H$ [bits/symbol] $\times$ $x$ [symbols/second] = $5$ [bits/second]

compute $x$.

  • $\begingroup$ how can you compute the entropy if the probabilities are not given? $\endgroup$ May 7, 2014 at 20:23
  • $\begingroup$ @user1930901: They are given. All symbols are equally likely. $\endgroup$
    – Matt L.
    May 7, 2014 at 20:24

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