Last class

Channel with feed-back

source channel separation

concatenated codes (again)

we have  

Source information k bits                                    

outer code Use the RS Code to do the encode 

n bits 

 \   log n     /

 to be able to encode the RS, R < 1-2p 

How many information symbols ?    ( n/ log n ) *(1-2p)

inner code : use the GV code to do the encode

the length of each symbol is  log n

n bits

 \   log n     /

For GV   R< 1- H(2p_2)

 the number of information symbols =  ( 1- H(2p_2))( n/ log n ) *(1-2p)

Channel

encode               encode          channel          decode            decode         

outer code    --   inner code     ---------->      inner code   --  outer code

Gaussion channel

fake channel : transmit n bits by real number

Power   -1. Too large:

            -2. Too small : lead noise.

case: r is transmited and a gaussion noise will be added in channel

r1 --> + --> r1 +N1 

        ^

         |

        N(0,)  => AWGN  (Addtive White Gaussion Noise) Channel

dfsf 

Message : 

average power constraint  :  

(in textbook   )

-------------------------------->           Channel    ----------------------->

The capacity of a Gaussion channel with power constraint P and noise variance N is

C = 1/2 log (1+P/N) bits

the radius of the big ball is

the radius  of the sphere is  

The maximum number of non-intersecting decoding spheres  is no more than  

and

The capacity =

                                                          ||               ||

                                                       h(X+n)       h(x+n|x)     since Y= X+N

                                                                           ||

                                                                         h(n) 

Given one particular message

 how to achive the max capacity? when X is N(0,P)