MinimumSum.m

%- Coded By,
      %Ganeshaanand (Rishi) Balasubramanian
      %MASc. Electrical and Computer Engineering
      %Dalhousie University
      %2018 - 2022
      
%------------------------------%----------------------------------%-----------------------------------%
%------------------------------MIN SUM DECODER-----------------------%
function vHat = MinimumSum(rx, H, iteration)

[M, N] = size(H);

% Prior log-likelihood (simplified). 
Lci = -rx;

% Initialization
Lrji = zeros(M, N);
Pibetaij = zeros(M, N);

% Asscociate the L(ci) matrix with non-zero elements of H
Lqij = H.*repmat(Lci, M, 1);

for n = 1:iteration
   %fprintf('Iteration : %d\n', n);
   
   % Get the sign and magnitude of L(qij)   
   alphaij = sign(Lqij);  
   betaij = abs(Lqij);

   % ----- Horizontal step -----
   for i = 1:M
      
      % Find non-zeros in the column
      c1 = find(H(i, :));
      
      % Get the minimum of betaij
      for k = 1:length(c1)
         
         % Minimum of betaij\c1(k)
         minOfbetaij = realmax;
         for l = 1:length(c1)
            if l ~= k  
               if betaij(i, c1(l)) < minOfbetaij
                  minOfbetaij = betaij(i, c1(l));
               end
            end           
         end % for l
                 
         % Multiplication alphaij\c1(k) (use '*' since alphaij are -1/1s)
         prodOfalphaij = prod(alphaij(i, c1))*alphaij(i, c1(k)); 
         
         % Update L(rji)
         Lrji(i, c1(k)) = prodOfalphaij*minOfbetaij;
      
      end % for k
      
   end % for i

   % ------ Vertical step ------
   for j = 1:N

      % Find non-zero in the row
      r1 = find(H(:, j));
      
      for k = 1:length(r1)         
         
         % Update L(qij) by summation of L(rij)\r1(k)
         Lqij(r1(k), j) = Lci(j) + sum(Lrji(r1, j)) - Lrji(r1(k), j);
      
      end % for k
      
      % Get L(Qij)
      LQi = Lci(j) + sum(Lrji(r1, j));
      
      % Decode L(Qi)
      if LQi < 0
         vHat(j) = 1;
      else
         vHat(j) = 0;
      end
                 
   end % for j
   
   %If arrived at proper codeword then break
   cs = mod(vHat*H',2);
    if sum(cs)== 0  
        break;
    end
end % for n