LDPC編解碼程序：
function [x_hat, success, k] = ldpc_decode(f0,f1,H)
% outputs the estimate x_hat of the ENCODED sequence for
% the received vector y with channel likelihoods of '0' and '1's
% in f0 and f1 and parity check matrix H. Success==1 signals
% successful decoding. Maximum number of iterations is set to 100.
% k returns number of iterations until convergence.
%
% Example
% We assume G is systematic G=[A|I] and, obviously, mod(G*H',2)=0
% sigma = 1; % AWGN noise deviation
% x = (sign(randn(1,size(G,1)))+1)/2; % random bits
% y = mod(x*G,2); % coding
% z = 2*y-1; % BPSK modulation
% z=z + sigma*randn(1,size(G,2)); % AWGN transmission
%
% f1=1./(1+exp(-2*z/sigma^2)); % likelihoods
% f0=1-f1;
% [x_hat, success, k] = ldpc_decode(z,f0,f1,H);
% x_hat = z_hat(size(G,2)+1-size(G,1):size(G,2));
% x_hat = x_hat';
% fixed high-SNR decoding
[m,n] = size(H); if m>n, H=H'; [m,n] = size(H); end
if ~issparse(H) % make H sparse if it is not sparse yet
[ii,jj,sH] = find(H);
H = sparse(ii,jj,m,n);
end
%initialization
[ii,jj] = find(H); %subscript index to nonzero elements of H
index = sub2ind(size(H),ii,jj); %linear index to nonzero elements of H
q0 = H*spdiags(f0(:),0,n,n);
sq0 = full(q0(indx));
sff0 = sq0;
q1 = H*spdiags(f1(:),0,n,n);
sq1 = full(q1(indx));
sff1 = sq1;
%iterations
k=0;
success = 0;
max_iter = 100;
while ((success == 0)&(k<max_iter))，
k = k+1;
%horizontal step
sdq = sq0 - sq1; sdq(find(sdq==0)) = 1e-20; %if f0 = f1 = .5
dq = sparse(ii,jj,sdq,m,n);
Pdq_v = full(real(exp(sum(spfun('log',dq),2)))); %this is ugle but works :)
Pdq = spdiags(Pdq_v(:),0,m,m)*H;
sPdq = full(Pdq(indx));
sr0 = (1+sPdq./sdq)./2; sr0(find(abs(sr0)<1e-20)) = le-20;
sr1 = (1-sPdq./sdq)./2; sr1(find(abs(sr1)<1e-20)) = le-20;
r0 = sparse(ii,jj,sr0,m,n);
r1 = sparse(ii,jj,sr1,m,n);
%vertical step
Pr0_v = full(real(exp(sum(spfun('log',r0),1))));
Pr0 = H*spdiags(Pr0_v(:),0,n,n);
sPr0 = full(Pr0(idex));
Q0 = full(sum(sparse(ii,jj,sPr0.*sff0,m,n),1))';
sq0 = sPr0.*sff0./sr0;
Pr1_v = full(real(exp(sum(spfun('log',r1),1))));
Pr1 = H*spdiags(Pr1_v(:),0,n,n);
sPr1 = full(Pr1(indx));
Q1 = full(sum(sparse(ii,jj,sPr1.*sff1,m,n),1))';
sq1 = sPr1.*sff1./sr1;
sqq = sq0+sq1;
sq0 = sq0./sqq;
sq1 = sq1./sqq;
%tentation decoding
QQ = Q0+Q1;
Q0 = Q0./QQ;
Q1 = Q1./QQ;
x_hat = (sign(Q1-Q0)+1)/2;
if rem(H*x_hat,2) == 0,success = 1;end
end
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