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)
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