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Shannon entropy problem

  1. Feb 10, 2010 #1
    consider a pack of 52 cards in a bridge game. a player try to convey 13 cards by nods of head or shake of heads to his partner. find the shannon entropy
     
  2. jcsd
  3. Feb 12, 2010 #2
    You need [itex]\rm{log}_{2}52 \approx 6 bits/card[/itex] to specify a single card (admitting that they are all equiprobable). For 13 independent cards, you'll need [itex]13\times\rm{log}_{2}52 bits[/itex].
     
  4. Feb 12, 2010 #3
    but the question tells the answer is 40, and it asks to find a coding function with entropy 50
     
  5. Feb 12, 2010 #4
    Well, then the question is asking for the amount of information necessary to transmit an arrangement of 13 cards as a whole and not individually; that was not clear from the question.

    There are [itex]\binom{52}{13}[/itex] possible arrangements, and this gives an entropy of [itex]-\rm{log_2}\binom{52}{13} \approx 39.21 bits[/itex].
     
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