lecture note 3

`     

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'Hôpital'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 <

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