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lecture notes 3

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Saved by Tong
on January 18, 2009 at 9:24:37 pm

lecture note 3


`      Formula

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



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




if ||p-q||  Formula we have Formula 


the number of  typical Formula 



Question :                Formula

               to prove   Formula


by l'Hôpital's rule, we haveFormula   



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)


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)



(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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