B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

864 ERROR CORRECTING CODES
Figure 14.25
Comparison of
bit error rates of
uncoded polar
signaling transmission
and
polar signaling
transmission of
Hamming (7, 4)
encoded
[(dashed) and
uncoded (solid)
message bits.
10 ° 0--------,--------r-----,--------,--- , -_-_-_-_-_--:....c-r_-_-_-_-_-_-_-_- ----,
-- - ---- - - .... .... .... .... .... ....
.... ,..,.
--- Uncoded
----- Coded
... " '''''''' ' ' '
\
\
\
\
\
\
\
\
\
\
\
\
10-7 -----------------------'-
2 4
6
Eb!N, dB
8 10 12
1 1 0 1 0 0 1] ;
E= [l 0 0 0 0 0 0
0 1 0 0 0 0 0
0 0 1 0 0 0 0
0 0 0 1 0 0 0
0 0 0 0 1 0 0
0 0 0 0 0 1 0
0 0 0 0 0 0 1
0 0 0 0 0 0 O J ;
K2=size (E,1) ;
Syndrome=mod (mtimes (E,H') ,2) ;
L1=25000;K=4*Ll;
% Error patterns
% Syndrome list
%Decide how many codewords
sig_b=round (rand (l,K) );
sig_2=reshape (sig_b,4,Ll) ;
xig_l=mod (G' *sig_2 ,2) ;
xig_2 =2* reshape (xig_l ,l, 7*Ll) -1;
AWnoisel=randn(l,7*Ll) ;
AWnoise2=randn(l,4*Ll) ;
% Change SNR and compute BER's
for ii=l :14
SNRdb=ii;
SNR=lO A (SNRdb*0.1) ;
xig_n=sqrt (SNR*4/7) *xig_2 +AWnoisel;
%Generate message bits
%4 per column for FEC
%Encode column by column
%P/S conversion
%Generate AWGN for coded Tx
%Generate AWGN for uncoded Tx
%Add AWGN and adjust SNR