function x_hat = func_Ldpc_dec(z,sigma,H);
f1 = 1./(1 + exp(-2*z/sigma^2));
f0 = 1 - f1;
[m,n] = size(H);
if m>n
H = H';
[m,n] = size(H);
end
if ~issparse(H)
[ii,jj,sH] = find(H);
H = sparse(ii,jj,sH,m,n);
end
[ii,jj] = find(H);
indx = sub2ind(size(H),ii,jj);
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;
k = 0;
success = 0;
max_iter = 20;
while ((success == 0) & (k < max_iter))
k = k+1;
sdq = sq0 - sq1;
sdq(find(sdq==0)) = 1e-20;
dq = sparse(ii,jj,sdq,m,n);
Pdq_v = full(real(exp(sum(spfun('log',dq),2))));
Pdq = spdiags(Pdq_v(:),0,m,m) * H;
sPdq = full(Pdq(indx));
sr0 = (1+sPdq./sdq)./2;
sr0(find(abs(sr0) < 1e-20)) = 1e-20;
sr1 = (1-sPdq./sdq)./2;
sr1(find(abs(sr1) < 1e-20)) = 1e-20;
r0 = sparse(ii,jj,sr0,m,n);
r1 = sparse(ii,jj,sr1,m,n);
Pr0_v = full(real(exp(sum(spfun('log',r0),1))));
Pr0 = H * spdiags(Pr0_v(:),0,n,n);
sPr0 = full(Pr0(indx));
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;
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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