How to calculate soft output for bpsk demodulator

I use BPSK modulator and de-modulator and for error correction i use LDPC. input for LDPC decoder should be soft out put (likelihood) not real value but to calculate this soft bit I have problem. below is my code, how to calculate the soft bit out put according to my BPSK modulation?

SNR=[-1 :1 ];
msgLength=1000;

for i=1:length(SNR)
    Nerr_ch(i) = 0;
    Nerr(i)=0;
    % Make random data (0/1)
    BitIn = round(rand(msgLength,1));

      % Encoding
      % in this part I use LDPC Encoding function
      BitEncode = BitIn;

      % BPSK modulation 0 -> -1; 1 -> 1
      bpskMod = 2*BitEncode - 1;

      sigma=10^(-SNR(i)/20);
      N0=1/sqrt(2)*(randn(msgLength,1)+1i*randn(msgLength,1));
      noise=sigma *N0 ;

      % Add noise
      rx = bpskMod+noise;

      % BPSK Demodulation

      *% in this line I have problem I suppose to multiple sigma and -1 to rx signal  
      % receiver - Soft decision decoding 
      Bitout_soft=-1*rx*sigma;* 

      % receiver - Hard decision decoding 
      BitOut=real(rx)>0;

      %Decoding
      BitDecode=Bitout_soft;

      % Channel errors
      [num1, rat1] = biterr(BitOut, BitEncode);
      Nerr_ch(i) = (Nerr_ch(i) + rat1);
      % Count errors of LDPC function
      [num2, rat2] = biterr(BitDecode, BitIn);
      Nerr(i) = (Nerr(i) + rat2); 
  end