function [soft_out,ex_info]=max_th(n,app)
%****************************************************************
% 內容概述：子譯碼器。
%          利用硬件化的方式實現TURBO碼的MAX-LOG-MAP譯碼
%          生成矩陣按照3GPP標準為[1 1 0 1;1 0 1 1]
%          輸入為經過高斯信道的RSC軟輸入，而輸出為軟輸出和外部信息
% 創 建 人：朱殿榮/QQ:235347/MSN:njzdr@msn.com
% 單    位：南京郵電大學，通信工程系
% 創建時間：2005年9月3日
% 修改時間：
% 參考文獻：《數字通信－－基礎與應用》
%          《改進的Turbo碼算法及其FPGA實現過程的研究》,天津大學，張寧，趙雅興
%           后向度量的計算方式和decoder_3GPP_MAX.m有所不同
% 版權聲明：任何人均可復制、傳播、修改此文件，同時需保留原始版權信息。
%****************************************************************
 
x=in(1,:);              %輸入系統位
y=in(2,:);              %輸入校驗位
in_length=length(in);
% Kw=0;

%---初始化&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
ln2=0.693147;               %超過門限后的max運算補償值
Infty = -128;
d=zeros(8,2,in_length);     %分支量度，8種可能狀態，輸入為0或者1
                            %D(S,i,k)
a=Infty*ones(8,in_length);  %前向分支量度，A(S,k)
a(1,1)=0;                   %寄存器狀態由全零開始
b=Infty*ones(8,in_length+1);%后向分支量度，B(S,k)
b(1,in_length)=0;           %寄存器狀態由全零結束

%---計算度量和LLR&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
for k=1:in_length
    d(1,2,k)=x(k)+y(k)+app(k);
    d(2,2,k)=d(1,2,k);
    d(7,2,k)=d(1,2,k);
    d(8,2,k)=d(1,2,k);
    
    d(3,2,k)=x(k)+app(k);
    d(4,2,k)=d(3,2,k);
    d(5,2,k)=d(3,2,k);
    d(6,2,k)=d(3,2,k);

    d(3,1,k)=y(k);
    d(4,1,k)=d(3,1,k);
    d(5,1,k)=d(3,1,k);
    d(6,1,k)=d(3,1,k);
    
    if k>1
        %a(1,k)=max((a(1,k-1)+d(1,1,k-1)),(a(2,k-1)+d(2,2,k-1)))+Kw;
        %a(2,k)=max((a(4,k-1)+d(4,1,k-1)),(a(3,k-1)+d(3,2,k-1)))+Kw;
        %a(3,k)=max((a(5,k-1)+d(5,1,k-1)),(a(6,k-1)+d(6,2,k-1)))+Kw;
        %a(4,k)=max((a(8,k-1)+d(8,1,k-1)),(a(7,k-1)+d(7,2,k-1)))+Kw;
        %a(5,k)=max((a(2,k-1)+d(2,1,k-1)),(a(1,k-1)+d(1,2,k-1)))+Kw;
        %a(6,k)=max((a(3,k-1)+d(3,1,k-1)),(a(4,k-1)+d(4,2,k-1)))+Kw;
        %a(7,k)=max((a(6,k-1)+d(6,1,k-1)),(a(5,k-1)+d(5,2,k-1)))+Kw;
        %a(8,k)=max((a(7,k-1)+d(7,1,k-1)),(a(8,k-1)+d(8,2,k-1)))+Kw;         
        a(1,k)=max(a(1,k-1),(a(2,k-1)+d(2,2,k-1)));
        if abs(a(1,k-1)-(a(2,k-1)+d(2,2,k-1)))<1
            a(1,k)=max(a(1,k-1),(a(2,k-1)+d(2,2,k-1)))+ln2;
        end
        a(2,k)=max((a(4,k-1)+d(4,1,k-1)),(a(3,k-1)+d(3,2,k-1)));
        a(3,k)=max((a(5,k-1)+d(5,1,k-1)),(a(6,k-1)+d(6,2,k-1)));
        a(4,k)=max(a(8,k-1),(a(7,k-1)+d(7,2,k-1)));
        a(5,k)=max(a(2,k-1),(a(1,k-1)+d(1,2,k-1)));
        a(6,k)=max((a(3,k-1)+d(3,1,k-1)),(a(4,k-1)+d(4,2,k-1)));
        a(7,k)=max((a(6,k-1)+d(6,1,k-1)),(a(5,k-1)+d(5,2,k-1)));
        a(8,k)=max(a(7,k-1),(a(8,k-1)+d(8,2,k-1)));      
    end
    
    if k==in_length
        %b(1,k)=max((b(1,k+1)+d(1,1,k)),(b(5,k+1)+d(1,2,k)))+Kw;
        %b(2,k)=max((b(5,k+1)+d(2,1,k)),(b(1,k+1)+d(2,2,k)))+Kw;
        %b(3,k)=max((b(6,k+1)+d(3,1,k)),(b(2,k+1)+d(3,2,k)))+Kw;
        %b(4,k)=max((b(2,k+1)+d(4,1,k)),(b(6,k+1)+d(4,2,k)))+Kw;
        %b(5,k)=max((b(3,k+1)+d(5,1,k)),(b(7,k+1)+d(5,2,k)))+Kw;
        %b(6,k)=max((b(7,k+1)+d(6,1,k)),(b(3,k+1)+d(6,2,k)))+Kw;
        %b(7,k)=max((b(8,k+1)+d(7,1,k)),(b(4,k+1)+d(7,2,k)))+Kw;
        %b(8,k)=max((b(4,k+1)+d(8,1,k)),(b(8,k+1)+d(8,2,k)))+Kw;

        b(1,k)=max(b(1,k+1),(b(5,k+1)+d(1,2,k)));
        b(2,k)=max(b(5,k+1),(b(1,k+1)+d(2,2,k)));
        b(3,k)=max((b(6,k+1)+d(3,1,k)),(b(2,k+1)+d(3,2,k)));
        b(4,k)=max((b(2,k+1)+d(4,1,k)),(b(6,k+1)+d(4,2,k)));
        b(5,k)=max((b(3,k+1)+d(5,1,k)),(b(7,k+1)+d(5,2,k)));
        b(6,k)=max((b(7,k+1)+d(6,1,k)),(b(3,k+1)+d(6,2,k)));
        b(7,k)=max(b(8,k+1),(b(4,k+1)+d(7,2,k)));
        b(8,k)=max(b(4,k+1),(b(8,k+1)+d(8,2,k)));

        %計算LLR--------------------------------------
        l(k)=max([...
            (a(1,k)+d(1,2,k)+b(5,k+1)),(a(2,k)+d(2,2,k)+b(1,k+1)),...
            (a(3,k)+d(3,2,k)+b(2,k+1)),(a(4,k)+d(4,2,k)+b(6,k+1)),...
            (a(5,k)+d(5,2,k)+b(7,k+1)),(a(6,k)+d(6,2,k)+b(3,k+1)),...
            (a(7,k)+d(7,2,k)+b(4,k+1)),(a(8,k)+d(8,2,k)+b(8,k+1))...
            ])-max([...
            (a(1,k)+b(1,k+1)),(a(2,k)+b(5,k+1)),...
            (a(3,k)+d(3,1,k)+b(6,k+1)),(a(4,k)+d(4,1,k)+b(2,k+1)),...
            (a(5,k)+d(5,1,k)+b(3,k+1)),(a(6,k)+d(6,1,k)+b(7,k+1)),...
            (a(7,k)+b(8,k+1)),(a(8,k)+b(4,k+1))...
            ]);
    end
end

for k=in_length-1:-1:1
        b(1,k)=max(b(1,k+1),(b(5,k+1)+d(1,2,k)));
        b(2,k)=max(b(5,k+1),(b(1,k+1)+d(2,2,k)));
        b(3,k)=max((b(6,k+1)+d(3,1,k)),(b(2,k+1)+d(3,2,k)));
        b(4,k)=max((b(2,k+1)+d(4,1,k)),(b(6,k+1)+d(4,2,k)));
        b(5,k)=max((b(3,k+1)+d(5,1,k)),(b(7,k+1)+d(5,2,k)));
        b(6,k)=max((b(7,k+1)+d(6,1,k)),(b(3,k+1)+d(6,2,k)));
        b(7,k)=max(b(8,k+1),(b(4,k+1)+d(7,2,k)));
        b(8,k)=max(b(4,k+1),(b(8,k+1)+d(8,2,k)));

        %計算LLR--------------------------------------
        l(k)=max([...
            (a(1,k)+d(1,2,k)+b(5,k+1)),(a(2,k)+d(2,2,k)+b(1,k+1)),...
            (a(3,k)+d(3,2,k)+b(2,k+1)),(a(4,k)+d(4,2,k)+b(6,k+1)),...
            (a(5,k)+d(5,2,k)+b(7,k+1)),(a(6,k)+d(6,2,k)+b(3,k+1)),...
            (a(7,k)+d(7,2,k)+b(4,k+1)),(a(8,k)+d(8,2,k)+b(8,k+1))...
            ])-max([...
            (a(1,k)+b(1,k+1)),(a(2,k)+b(5,k+1)),...
            (a(3,k)+d(3,1,k)+b(6,k+1)),(a(4,k)+d(4,1,k)+b(2,k+1)),...
            (a(5,k)+d(5,1,k)+b(3,k+1)),(a(6,k)+d(6,1,k)+b(7,k+1)),...
            (a(7,k)+b(8,k+1)),(a(8,k)+b(4,k+1))...
            ]);
   %計算LLR--------------------------------------
%   l(k)=max([...
%       (a(1,k)+d(1,2,k)+b(5,k+1)),(a(2,k)+d(2,2,k)+b(1,k+1)),...
%       (a(3,k)+d(3,2,k)+b(2,k+1)),(a(4,k)+d(4,2,k)+b(6,k+1)),...
%       (a(5,k)+d(5,2,k)+b(7,k+1)),(a(6,k)+d(6,2,k)+b(3,k+1)),...
%       (a(7,k)+d(7,2,k)+b(4,k+1)),(a(8,k)+d(8,2,k)+b(8,k+1))...
%       ])-max([...
%       (a(1,k)+d(1,1,k)+b(1,k+1)),(a(2,k)+d(2,1,k)+b(5,k+1)),...
%       (a(3,k)+d(3,1,k)+b(6,k+1)),(a(4,k)+d(4,1,k)+b(2,k+1)),...
%       (a(5,k)+d(5,1,k)+b(3,k+1)),(a(6,k)+d(6,1,k)+b(7,k+1)),...
%       (a(7,k)+d(7,1,k)+b(8,k+1)),(a(8,k)+d(8,1,k)+b(4,k+1))...
%       ]); 
end
soft_out=l;
ex_info=soft_out-app-x;