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

References 865
rig_l= (l+sign ( xig_n) )/2;
r=reshape (rig_l ,7,Ll) ';
x=mod (r*H' , 2) ;
for kl=l :Ll,
for k2=1 :K2,
if Syndrome (k2, :)==x (kl, :),
idxe=k2 ;
end
end
error=E ( idxe , : ) ;
cword=xor (r(kl, :),error) ;
sigcw( :,kl)=cword(l:4) ;
end
cw=reshape (sigcw, 1,K) ;
BER_coded (ii) =sum ( abs (cw-sig_b ) )/K;
%Hard decisions
%S/P to form 7 bit codewords
% generate error syndromes
%find the Syndrome index
%look up the error pattern
%error correction
%keep the message bits
% Coded BER on info bits
% Uncoded Simulation Without Hamming code
xig_3 =2*sig_b- 1;
% Polar signaling
xig_m=sqrt (SNR) *xig_3 +AWnoise2 ;
% Add AWGN and adj ust SNR
rig_l= (l+sign ( xig_m) )/2;
% Hard decision
BER_uncode (ii) =sum(abs ( rig_l-sig_b) ) /K; % Compute BER
end
EboverN= [l:14] -3 ; % Need to note that SNR = 2 Eb/N
Naturally, when the E b / JV is low, there tends to be more than 1 error bit per codeword. Thus, when
there is more than 1 bit error, the decoder will still consider the codeword to be corrupted by only 1 bit
error. Its attempt to correct 1-bit error may in fact add an error bit. When the E b / N is high, it is more
likely that a codeword has at most 1 bit error. This explains why the coded BER is worse at lower E b / N
and better at higher E b / N. On other other hand, Fig. 14.3 gives an optimistic approximation by assuming
a cognitive decoder that will take no action when the number of bit errors in each codeword exceeds 1.
Its performance is marginally better at low E b / N ratio.
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