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Scribe Notes 6-4

last edited by 13 years, 4 months ago

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)