0
$\begingroup$

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?

$\endgroup$
  • $\begingroup$ It would be nice if you write also what you may have thought or tried to do. $\endgroup$ – FELIPE_RIBAS May 7 '14 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 $\endgroup$ – user1930901 May 7 '14 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 '14 at 20:23
3
$\begingroup$

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 $x$.

$\endgroup$
  • $\begingroup$ how can you compute the entropy if the probabilities are not given? $\endgroup$ – user1930901 May 7 '14 at 20:23
  • $\begingroup$ @user1930901: They are given. All symbols are equally likely. $\endgroup$ – Matt L. May 7 '14 at 20:24

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.