function [decoder_output,survivor_state,cumulated_metric]=viterbip(G,k,channel_output,P)%VITERBI	The Viterbi decoder for convolutional codes%		[decoder_output,survivor_state,cumulated_metric]=viterbi(G,k,channel_output)%		G is a n x Lk matrix each row of which%          	determines the connections from the shift register to the%          	n-th output of the code, k/n is the rate of the code.%          	survivor_state is a matrix showing the optimal path through%          	the trellis. The metric is given in a separate function metric(x,y)%          	and can be specified to accomodate hard and soft decision.%          	This algorithm minimizes the metric rather than maximizing%          	the likelihood.%        P is puncture matrixn=size(G,1);[r,c]=size(P);punc=reshape(P,1,r*c);position_P0=find(~punc);  %取0的位置如P=[1 1;1 0];position_P0＝4；目前程序中還未用position_P0%  check the sizesif rem(size(G,2),k) ~=0   error('Size of G and k do not agree')endif rem(size(channel_output,2),n) ~=0  error('channel output not of the right size')endL=size(G,2)/k;number_of_states=2^((L-1)*k);%  generate state transition matrix, output matrix, and input matrixfor j=0:number_of_states-1  for l=0:2^k-1    [next_state,memory_contents]=nxt_stat(j,l,L,k);    input(j+1,next_state+1)=l;    branch_output=rem(memory_contents*G',2);    nextstate(j+1,l+1)=next_state;    output(j+1,l+1)=bin2deci(branch_output);  endendstate_metric=zeros(number_of_states,2);depth_of_trellis=length(channel_output)/n;channel_output_matrix=reshape(channel_output,n,depth_of_trellis);survivor_state=zeros(number_of_states,depth_of_trellis+1);%  start decoding of non-tail channel outputsfor i=1:depth_of_trellis-L+1  flag=zeros(1,number_of_states);  if i <= L    step=2^((L-i)*k);  else    step=1;  end  for j=0:step:number_of_states-1    for l=0:2^k-1      branch_metric=0;      binary_output=deci2bin(output(j+1,l+1),n);            for ll=1:n          %if (rem(i,2)==0) &(ll==2)    %rc=2/3 %判斷是否是刪除的位置，若是，則metric=0；不是，則計算metric          if (rem(i+1,3)==0) &(ll==2) | (rem(i+0,3)==0) &(ll==2)  %rc=3/4                branch_metric=branch_metric+0;                      else              branch_metric=branch_metric+metric(channel_output_matrix(ll,i),binary_output(ll));          end%          branch_metric=branch_metric+metric(channel_output_matrix(ll,i),binary_output(ll));       end      if((state_metric(nextstate(j+1,l+1)+1,2) > state_metric(j+1,1)...        +branch_metric) | flag(nextstate(j+1,l+1)+1)==0)        state_metric(nextstate(j+1,l+1)+1,2) = state_metric(j+1,1)+branch_metric;        survivor_state(nextstate(j+1,l+1)+1,i+1)=j;        flag(nextstate(j+1,l+1)+1)=1;      end    end  end  state_metric=state_metric(:,2:-1:1);end%  start decoding of the tail channel-outputsfor i=depth_of_trellis-L+2:depth_of_trellis  flag=zeros(1,number_of_states);  last_stop=number_of_states/(2^((i-depth_of_trellis+L-2)*k));  for j=0:last_stop-1      branch_metric=0;      binary_output=deci2bin(output(j+1,1),n);      for ll=1:n         %if  (rem(i,2)==0) &(ll==2)  %rc=2/3          if  (rem(i+1,3)==0) &(ll==2) | (rem(i+0,3)==0) &(ll==2)  %rc=3/4            branch_metric=branch_metric+0;        else            branch_metric=branch_metric+metric(channel_output_matrix(ll,i),binary_output(ll));        end%             branch_metric=branch_metric+metric(channel_output_matrix(ll,i),binary_output(ll));      end      if((state_metric(nextstate(j+1,1)+1,2) > state_metric(j+1,1)...        +branch_metric) | flag(nextstate(j+1,1)+1)==0)        state_metric(nextstate(j+1,1)+1,2) = state_metric(j+1,1)+branch_metric;        survivor_state(nextstate(j+1,1)+1,i+1)=j;        flag(nextstate(j+1,1)+1)=1;      end  end  state_metric=state_metric(:,2:-1:1);end%  generate the decoder output from the optimal pathstate_sequence=zeros(1,depth_of_trellis+1);state_sequence(1,depth_of_trellis)=survivor_state(1,depth_of_trellis+1);for i=1:depth_of_trellis  state_sequence(1,depth_of_trellis-i+1)=survivor_state((state_sequence(1,depth_of_trellis+2-i)...  +1),depth_of_trellis-i+2);enddecodeder_output_matrix=zeros(k,depth_of_trellis-L+1);for i=1:depth_of_trellis-L+1  dec_output_deci=input(state_sequence(1,i)+1,state_sequence(1,i+1)+1);  dec_output_bin=deci2bin(dec_output_deci,k);  decoder_output_matrix(:,i)=dec_output_bin(k:-1:1)';enddecoder_output=reshape(decoder_output_matrix,1,k*(depth_of_trellis-L+1));cumulated_metric=state_metric(1,1);