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Help with entropy calculation (binary erasure channel)

  1. Mar 11, 2008 #1

    Simfish

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    So in a binary erasure channel, the book says that H(Y) [of the output] = H((1-p)(1-a),a,p(1-a)) = H(a) + (1-a)H(p), where p = Pr (X=1) [rather than X = 0] and a is the probability that ANY input of X would be erased. the problem is, how do you get from H((1-p)(1-a),a,p(1-a)) = H(a) + (1-a)H(p),? there are 3 inputs to the entropy function and they're not independent (I think) so you can't just brute force the entropy algorithm. The main thing I'm confused about is how do you get (1-a)H(p), with the (1-a) term outside of the entropy term?
     
  2. jcsd
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