function outer_out_c=outer_decode_c(outer_input,trellis,formerstate)
% this function does the iterative MAP decode process of the
% outer convolutional code

number_of_states=trellis.numStates;
nextstate=trellis.nextStates;
fanout=trellis.numInputSymbols;
output=trellis.outputs;
number_of_out=trellis.numOutputSymbols;
depth_of_trellis=size(outer_input,2);

alpha=zeros(number_of_states,depth_of_trellis);
alpha(:,1)=[0;-1e10*ones(number_of_states-1,1)];
alpha1=zeros(1,fanout);
gamma=zeros(fanout,depth_of_trellis);
max=-1e10*ones(1,depth_of_trellis-1);
beta=zeros(number_of_states,depth_of_trellis);
beta(:,depth_of_trellis)=[0;-1e10*ones(number_of_states-1,1)];
beta1=zeros(1,fanout);
lu=zeros(number_of_out-1,depth_of_trellis); 

% forward recursion
for i=1:depth_of_trellis-1
    for j=1:number_of_states
        for k=1:fanout
            if(formerstate(j,1,k)~=number_of_states)
                for h=1:fanout
                    t=output(formerstate(j,h,k)+1,k)+1;
                    if(t~=number_of_out)
                        gamma(h,i)=outer_input(t,i);
                    else
                        gamma(h,i)=0;
                    end
                    alpha1(h)=alpha(formerstate(j,h,k)+1,i)+gamma(h,i);
                    if(alpha1(h)<=-80)
                        alpha1(h)=0;
                    else
                        alpha1(h)=exp(alpha1(h));
                    end
                end
                if(sum(alpha1)>1e-30)
                     alpha(j,i+1)=log(sum(alpha1));
                else
                     alpha(j,i+1)=-1e10;
                end
                if(max(i)<alpha(j,i+1))
                     max(i)=alpha(j,i+1);
                end
            end
        end
    end
    alpha(:,i+1)=alpha(:,i+1)-max(i);
end

% backward recursion and compute the log-likelihood ratio
for i=depth_of_trellis:-1:1
    temp=zeros(1,number_of_out);
    for j=1:number_of_states
        for k=1:fanout
            t=output(j,k)+1;
            if(t~=number_of_out)
                gamma(k,i)=outer_input(t,i);
            else
                gamma(k,i)=0;
            end
            beta1(k)=beta(nextstate(j,k)+1,i)+gamma(k,i);
            if(beta1(k)<=-80)
                beta1(k)=0;
            else
                beta1(k)=exp(beta1(k));
            end
            temp(t)=temp(t)+exp(alpha(j,i)+gamma(k,i)+beta(nextstate(j,k)+1,i));
        end
        if(i>1)
            if(sum(beta1)>1e-30)
                beta(j,i-1)=log(sum(beta1))-max(i-1);
            else
                beta(j,i-1)=-1e10;
            end
        end
    end
    for h=1:number_of_out-1
        if(temp(h)==0)
            lu(h,i)=-100;
        elseif(temp(number_of_out)==0)
            lu(h,i)=log(temp(h))+100;
        else
            lu(h,i)=log(temp(h)/temp(number_of_out));
        end
        if(lu(h,i)>80)
            lu(h,i)=80;
        elseif(lu(h,i)<-80)
            lu(h,i)=-80;
        end
        outer_out_c(h,i)=lu(h,i)-outer_input(h,i);
        
    end
end
%outer_out_c=lu-outer_input;