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lecture notes 3

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Saved by Tong
on January 18, 2009 at 9:34:52 pm
 

lecture note 3

      Formula

`      Formula

Since Formula is very small, from the right-hand side of the inequality we have Formula 

          Formula

 

Definition(From the textbook): the relative entropy between two probability mass functions p(x) and q(x) is defined as

Formula.(divergence)

 

 

if ||p-q||  Formula we have Formula 

 

the number of  typical Formula 

               Formula

               Formula

Question :                Formula

               to prove   Formula

 

by l'Hôpital's rule, we haveFormula   

                                  Formula  

 

the number of the typical type-class Formula and the number of the typical element Formula

the size of largest set class Formula  

Expected # bits  (the typical part + the atypical part)

 Formula

the typical set decrease, as the epsilon decrease.

 

p <1/2 and n =10 in the following figures

Fig1: the relation between #of heads and probability,

Fig2: between # of heads and size of T(k,n)

  

the largest value of T(k,n) = T(n/2, n)   when k =n/2

Most likely of T(k,n) = T(np, n), when k=np

 

BSCT

(a) Formula,Formulacode with expected rate Formula

(b) Formula code with Formulaand expected rate < Formula

 

For General case(i  try my best to recall, but... Sorry here i just show a ref about source coding theorem) 

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