lecture note 3

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

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

.(divergence)

if ||p-q|| we have

the number of typical

Question :

to prove

by **l'HÃ´pital's rule, we have **

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

the size of largest set class

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)

BSCT

(a) ,code with expected rate

(b) code with and expected rate <

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