function L_all = sova(rec_s, g, L_a, ind_dec) 
% This function implememts Soft Output Viterbi Algorithm in trace back mode 
% Input: 
%       rec_s: scaled received bits. rec_s(k) = 0.5 * L_c(k) * y(k) 
%              L_c = 4 * a * Es/No, reliability value of the channel
%              y: received bits
%       g:  encoder generator matrix in binary form, g(1,:) for feedback, g(2,:) for feedforward
%       L_a: a priori information about the info. bits. Extrinsic info. from the previous
%             component decoder
%       ind_dec: index of the component decoder. 
%	          =1: component decoder 1; The trellis is terminated to all zero state
%    	          =2: component decoder 2; The trellis is not perfectly terminated.
% Output:
%       L_all: log ( P(x=1|y) ) / ( P(x=-1|y) )
%
% Copyright: Yufei Wu, Nov. 1998
% MPRG lab, Virginia Tech
% for academic use only

% Frame size, info. + tail bits
L_total = length(L_a);
[n,K] = size(g); 
m = K - 1;
nstates = 2^m;
Infty = 1e10;

% SOVA window size. Make decision after 'delta' delay. Decide bit k when received bits
% for bit (k+delta) are processed. Trace back from (k+delta) to k. 
% why set delta=30,not 40,10,20?    -yzh
delta = 30;    

% Set up the trellis defined by g.
[next_out, next_state, last_out, last_state] = trellis(g);

% Initialize path metrics to -Infty
for t=1:L_total+1
   for state=1:nstates
      path_metric(state,t) = -Infty;
   end
end
% Why not use "path_metric=zeros(nstates,L_total+1)"?   -yzh

% Trace forward to compute all the path metrics
path_metric(1,1) = 0;   % why path_metric(1,1) is set to 0? -yzh
for t=1:L_total
    % received bits at time t   -yzh
   y = rec_s(2*t-1:2*t);
   % state: current state of decoder register   -yzh
   for state=1:nstates  % state: vector,states start from step t+1, trace back from last state(step t)    --yzh
      sym0 = last_out(state,1:2);
      sym1 = last_out(state,3:4);
      state0 = last_state(state,1);
      state1 = last_state(state,2);
      % Mk0/Mk1: metric of state at time t  -yzh
      % y*sym0'/y*smy1': reliability is related to the amplitude of received bits
      % -yzh
      Mk0 = y*sym0' - L_a(t)/2 + path_metric(state0,t); % not lne function?     -yzh
      Mk1 = y*sym1' + L_a(t)/2 + path_metric(state1,t); % why +L_a(t)/2? received bit is 1(+1)   -yzh
      
      if Mk0>Mk1
         path_metric(state,t+1)=Mk0;
         Mdiff(state,t+1) = Mk0 - Mk1;
         prev_bit(state, t+1) = 0;  % decide the input bit -yzh
      else
         path_metric(state,t+1)=Mk1;
         Mdiff(state,t+1) = Mk1 - Mk0;
         prev_bit(state,t+1) = 1;   % decide the input bit -yzh
      end

   end
end
      
% For decoder 1, trace back from all zero state, 
% for decoder two, trace back from the most likely state
% Why decoder 1 trace back from zero state and 2 trace back from the most likely state? see encoderm.m and rsc_encode.m for answer    -yzh
% mlstate: Maximum likelihood state?    -yzh
if ind_dec == 1
   mlstate(L_total+1) = 1;
else
   % find( path_metric(:,L_total+1)==max(path_metric(:,L_total+1)) ) :
   % return the row number of the max value of L_total column   -yzh
   % the row number is the state, see the definition of path_metric  -yzh
   mlstate(L_total+1) = find( path_metric(:,L_total+1)==max(path_metric(:,L_total+1)) );
end

% Trace back to get the estimated bits, and the most likely path
for t=L_total:-1:1
   est(t) = prev_bit(mlstate(t+1),t+1);
   mlstate(t) = last_state(mlstate(t+1), est(t)+1);
end

% Find the minimum delta that corresponds to a competition path with different info. bit estimation.       
% Give the soft output
% delta: what's the meaning?    -yzh
for t=1:L_total
   llr = Infty;
   % i should from 1 to delta,i=0 is no meaning?  -yzh
   for i=0:delta    
      if t+i<L_total+1  % if t+i>L_total+1 will not track back?
         bit = 1-est(t+i);  % another competition path's output.  -yzh
         temp_state = last_state(mlstate(t+i+1), bit+1);    % why is mlstate(t+i+1),not mlstate(t+i)?   -yzh
         for j=i-1:-1:0 % % find competition path from temp_state defined above
            bit = prev_bit(temp_state,t+j+1);   % trace back for the competition path  -yzh
            temp_state = last_state(temp_state, bit+1); % trace back for the competition path  -yzh
         end
         if bit~=est(t) 
            llr = min( llr,Mdiff(mlstate(t+i+1), t+i+1) );  % Why is llr calculated in this way?  -yzh
            % see <A primer on turbo code concept> page 6, equation (50)
            % -yzh
         end
      end
   end
   L_all(t) = (2*est(t) - 1) * llr; % Why is L_all(t) calculated in this way?  -yzh
end