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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.  
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 
 
% Trace forward to compute all the path metrics 
path_metric(1,1) = 0; 
for t=1:L_total 
   y = rec_s(2*t-1:2*t); 
   for state=1:nstates 
      sym0 = last_out(state,1:2); 
      sym1 = last_out(state,3:4); 
      state0 = last_state(state,1); 
      state1 = last_state(state,2); 
      Mk0 = y*sym0' - L_a(t)/2 + path_metric(state0,t); 
      Mk1 = y*sym1' + L_a(t)/2 + path_metric(state1,t); 
       
      if Mk0>Mk1 
         path_metric(state,t+1)=Mk0; 
         Mdiff(state,t+1) = Mk0 - Mk1; 
         prev_bit(state, t+1) = 0; 
      else 
         path_metric(state,t+1)=Mk1; 
         Mdiff(state,t+1) = Mk1 - Mk0; 
         prev_bit(state,t+1) = 1; 
      end 
 
   end 
end 
       
% For decoder 1, trace back from all zero state,  
% for decoder two, trace back from the most likely state 
if ind_dec == 1 
   mlstate(L_total+1) = 1; 
else 
   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 compitition path with different info. bit estimation.        
% Give the soft output 
for t=1:L_total 
   llr = Infty; 
   for i=0:delta 
      if t+i