log likelihood ratio to probability measure

Question

xplore29 2013-5-19

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/76285-log-likelihood-ratio-to-probability-measure

For BPSK, one can theoretically move back and forth between log-likelihood ratio and probabilities by using following expressions

P(0) = 1/(1+exp(L)),P(1)=exp(L)/(1+exp(L)).

But in simulations if 'L' gets really large the above expression for P(1) returns NaN. Theory suggests that if L>>1, then P(1)-->1. I tried different values of L for which P(1) changes and found out that any value of L<-10 gives P(0)=1 and L>10 gives P(1)=1. I wrote the following two codes to compute P(0) and P(1)

%-----------------------Code-A--------------------------------- [row col] = size(LLR) for i=1:row for j=1:col

        if LLR(i,j)==+inf
            Probability(i,j) = 1;
        else
            Probability(i,j) = exp(LLR(i,j))/(1+exp(LLR(i,j)));
        end
    end
end
%-----------------------Code-B---------------------------------
 for i=1:row
     for j=1:col
         if LLR(i,j)>10
             Probability(i,j) = 1;
         end
         if LLR(i,j)<-10
             Probability(i,j) = -1;
         end
         if (LLR(i,j)<10)&&(LLR(i,j)>-10)
             Probability(i,j) = exp(LLR(i,j))/(1+exp(LLR(i,j)));
         end
     end
end
%--------------------------------------------------------------