function?[z_hat]?=?ldpc_decode（zHsigmaiteration）
%?Log-domain?sum?product?algorithm?LDPC?decoder對數域BP譯碼算法
%
%??z???????:?Received?signal?vector?（column?vector）?接收信號
%??H?????????:?LDPC?matrix?LDPC矩陣
%??N0??????:?Noise?variance?噪聲方差
%??iteration?:?Number?of?iteration?迭代次數
%
%??z_hat????:?Decoded?vector?（0/1）?
%
%
%?Copyright?Bagawan?S.?Nugroho?2007?
%?http://bsnugroho.googlepages.com

[mn]?=?size（H）;?if?m>n?H=H‘;?[mn]?=?size（H）;?end
if?~issparse（H）?%?make?H?sparse?if?it?is?not?sparse?yet如果不是稀疏矩陣，將H變為稀疏矩陣
???[iijjsH]?=?find（H）;
???H?=?sparse（iijjsHmn）;
end

%?Prior?log-likelihood.?Minus?sign?is?used?for?0/1?to?-1/1?mapping

qij1=1./（1+exp（-2*z./（sigma^2）））;
qij0=1-qij1;
Lci?=log（qij0./qij1）;
%?Initialization
Lrji?=?zeros（mn）;
Pibetaij?=?zeros（m?n）;

%?Asscociate?the?L（ci）?matrix?with?non-zero?elements?of
?Lqij?=?H.*repmat（Lcim?1）;

%?Get?non-zero?elements
[r?c]?=?find（H）;%r是行中非零元素，c是列中的非零元素

%?Iteration
for?u?=?1:iteration
???
%????fprintf（‘Iteration?:?%d\u‘?u）;
???
???%?Get?the?sign?and?magnitude?of?L（qij）???
???alphaij?=?sign（Lqij）;?
???betaij?=?abs（Lqij）;

???for?l?=?1:length（r）
??????Pibetaij（r（l）?c（l））?=?log（（exp（betaij（r（l）?c（l）））?+?1）/...
?????????????????????????????（exp（betaij（r（l）?c（l）））?-?1））;
???end
???
???%?-----?Horizontal?step校驗節點處理?-----
???for?i?=?1:m??
??????c1?=?find（H（i?:））;???%??找出列中的非零元素個數
??????
??????%?Get?the?summation?of?Pi（betaij））????????
??????for?k?=?1:length（c1）

?????????sumOfPibetaij?=?0;
?????????prodOfalphaij?=?1;
?????????
?????????%?Summation?of?Pi（betaij）\c1（k）
?????????sumOfPibetaij?=?sum（Pibetaij（i?c1））?-?Pibetaij（i?c1（k））;
?????????
?????????%?Avoid?division?by?zero/very?small?number?get?Pi（sum（Pi（betaij）））
?????????if?sumOfPibetaij?????????????sumOfPibetaij?=?1e-10;
?????????end?????????
?????????PiSumOfPibetaij?=?log（（exp（sumOfPibetaij）?+?1）/（exp（sumOfPibetaij）?-?1））;
??????
?????????%?Multiplication?of?alphaij\c1（k）?（use?‘*‘?since?alphaij?are?-1/1s）
?????????prodOfalphaij?=?prod（alphaij（i?c1））*alphaij（i?c1（k））;?%?prod使元素按列相乘????????????????
?????????%?Update?L（rji）?更新校驗節點
?????????Lrji（i?c1（k））?=?prodOfalphaij*PiSumOfPibetaij;
?????????
??????end?%?for?k
??????
???end?%?for?i
??soft_information=[];
???%?------?Vertical?step比特節點處理?------
???for?j?=?1:n

??????%?Find?non-zero?in?the?row
??????r1?=?find（H（:?j））;?%?找出行中的非零元素個數
??????
??????for?k?=?1:length（r1）????????
????????
?????????%?Update?L（qij）?by?summation?of?L（rij）\r1（k）
?????????Lqij（r1（k）?j）?=?Lci（j）?+?sum（Lrji（r1?j））?-?Lrji（r1（k）?j）;
??????
??????end?%?for?k
??????
??????%?Get?L（Qi）
??????LQi?=?Lci（j）?+?sum（Lrji（r1?j））;
??
???????
??????%?Decode?L（Qi）
??????if?LQi?<=?0
?????????z_hat（j）?=?1;
??????else
?????????z_hat（j）?=?0;
??????end
???????????????????
???end?%?for?j

????if?mod（z_hat*H‘2）?==?0?
????end
end?%?for?u


??

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件???????3025??2011-03-10?17:44??ldpc_decode.m

-----------?---------??----------?-----??----

?????????????????3025????????????????????1