function?[?outputdecode?]?=?SPA_decode（?H??r_num??c_num??EbN0??Rs?）
%SPA_decode?this?function?is?used?to?decode?LDPC?codes?with?SPA?method.
%???input:?H?--------the?check?matrix
%??????????c_num-----how?many?columns?in?H
%??????????r_num-----how?many?rows?in?H
%??????????EbNo------EbN0?for?the?AWGN?channel?which?is?used?to?calculate?log（p1/p0）
%??????????Rs--------receive?signals
%???output:?outputdecode-----the?decode?result?which?is?only?0s?and?1s

Receive?=?2?*?Rs?*?2?*?EbN0;?%%?假定信號功率為1;

%%%%%%%%%%%%%%%?set?parameter?%%%%%%%%%%%%%%%%%%%%%
????????it_num?=?20;?%iteration?number
????????row_nonzero_index?=?zeros（r_numc_num）;?%H中每行里1的位置
????????col_nonzero_index?=?zeros（r_numc_num）;?%H中每列里1的位置
????????row_nonzero_number?=?zeros（r_num1）;?%H中每行1的個數
????????col_nonzero_number?=?zeros（c_num1）;?%H中每列1的個數
????????u_ml?=?zeros（r_numc_num）;?%校驗節點（對校驗節點的更新值）
????????v_ml?=?zeros（r_numc_num）;?%變量節點（對變量節點的更新值）
????????v_l?=?zeros（1c_num）;?%似后驗概率
????????v_l0?=?zeros（1c_num）;?%初始后驗概率信息
?%%%%%%%%%%%%%%%?initialization?%%%%%%%%%%%%%%%%%%%%
????????%?找到每行中1的位置
????????for?i?=?1:r_num
????????????row_nonzero_number（i）?=?length（find（H（i:）））;
????????????row_nonzero_index（i:）?=?[find（H（i:））??zeros（1c_num-row_nonzero_number（i））];
????????end
????????%?找到每列中1的位置
????????for?j?=?1:c_num
????????????col_nonzero_number（j）?=?length（find（H（:j）））;
????????????col_nonzero_index（:j）?=?[find（H（:j））?;?zeros（r_num-col_nonzero_number（j）1）];
????????end
????????
????????v_l0?=?Receive;

????????for?i?=?1:r_num??%?it?can?be?better?here?by?using?column?assignment?%%%
????????????for?l?=?1:row_nonzero_number（i）
????????????????j?=?row_nonzero_index（il）;
????????????????v_ml（ij）?=?v_l0（j）;
????????????end?%?end?l
????????end?%?end?i
?%%%%%%%%%%%%%%%%%??iteration?%%%%%%%%%%%%%%%%%
????????for?it_counter?=?1:it_num
????????????%%%%%%?check?notes（u_ml）?updating?%%%%%%
????????????
????????????
%?????????????tanh_v_ml?=?tanh（v_ml/2）;
%?????????????for?i?=?1:r_num
%?????????????????len?=?row_nonzero_number（i）;
%?????????????????for?l?=?1:len
%?????????????????????j?=?row_nonzero_index（il）;
%?????????????????????pro?=?1;
%?????????????????????for?k?=1:len
%?????????????????????????if?k?~=?l
%?????????????????????????????pro?=?pro?*?tanh_v_ml（irow_nonzero_index（ik））;
%?????????????????????????end?%?end?if
%?????????????????????end?%?end?k?
%?????????????????????u_ml（ij）?=?2*atanh（pro）;
%?????????????????????why_error?=?double（isinf（u_ml（ij）））;
%?????????????????????if?why_error?~=?0
%?????????????????????????u_ml（ij）?=?sign（u_ml（ij））*1000;
%