function?[x_hat?success?k]?=?ldpc_decode（f0f1H）
%?decoding?of?binary?LDPC?as?in?Elec.?Letters?by?MacKay&Neal?13March1997
%?For?notations?see?the?same?reference.
%?function?[x_hat?success?k]?=?ldpc_decode（yf0f1H）
%?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（重復迭代）?is?set?to?100.
%?k?returns?number?of?iterations?until?convergence（收斂）.
%
%?Example:
%?We?assume?G?is?systematic?G=[A|I]?and?obviously?mod（G*H‘2）=0
%?????????sigma?=?1;??????????????????????????%?AWGN?noise?deviation
%?????????x?=?（sign（randn（1size（G1）））+1）/2;?%?random?bits
%?????????y?=?mod（x*G2）;?????????????????????%?coding?
%?????????z?=?2*y-1;??????????????????????????%?BPSK?modulation
%?????????z=z?+?sigma*randn（1size（G2））;?????%?AWGN?transmission
%
%?????????f1=1./（1+exp（-2*z/sigma^2））;????????%?likelihoods?
%?????????by蘭朋朋?./矩陣元素右除?A./B表示A（ij）/B（ij）
%?????????f0=1-f1;
%?????????[z_hat?success?k]?=?ldpc_decode（zf0f1H）;
%?????????x_hat?=?z_hat（size（G2）+1-size（G1）:size（G2））;
%?????????x_hat?=?x_hat‘;?

%???Copyright?（c）?1999?by?Igor?Kozintsev?igor@ifp.uiuc.edu
%???$Revision:?1.1?$??$Date:?1999/07/11?$
%???fixed?high-SNR?decoding

[mn]?=?size（H）;
if?m>n?
????H=H‘;?
????[mn]?=?size（H）;?
end
if?~issparse（H）?%?make?H?sparse?if?it?is?not?sparse?yet，%by蘭朋朋?函數的功能是如果該函數不是稀疏矩陣，就把它轉化為稀疏矩陣
%by蘭朋朋?在MATLAB中，issparse函數用于判斷一個稀疏矩陣存儲方式是否是sparse?storage?organization
%by蘭朋朋?如果稀疏矩陣的存儲方式是sparse?storage?organization，則返回邏輯1；否則返回邏輯0。
???[iijjsH]?=?find（H）;
%by蘭朋朋?返回矩陣H中的非零元素所在的行ii和所在的列jj和矩陣的非零元素sH
???H?=?sparse（iijjsHmn）;
%by蘭朋朋?[ijs]?=?find（S）;
%by蘭朋朋?[mn]?=?size（S）;
%by蘭朋朋?S?=?sparse（ijsmn）;???
end

%by蘭朋朋?BP譯碼算法
%initialization（沒看懂）
[iijj]?=?find（H）;?????????????%?subscript?index?to?nonzero?eleme