viterbi.m

Viterbi Algorithm & Viterbi Decoder Matlab Code.(Provided both soft & hard decision ability). Note:

function [decoder_output,survivor_state,cumulated_metric]=viterbi(G,k,channel_output)
%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.
 
n=size(G,1);
%  check the sizes
if rem(size(G,2),k) ~=0 
  error('Size of G and k do not agree')
end
if rem(size(channel_output,2),n)~=0
  error('channel output not of the right size')
end

L=size(G,2)/k;
number_of_states=2^((L-1)*k);

%==========================================================================
% (1) generate state transition matrix, output matrix, and input matrix
for 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);
  end
end
state_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);

%==========================================================================
% (2) start decoding of non-tail channel outputs
for 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
        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

%==========================================================================
% (3) start decoding of the tail channel-outputs
for 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
        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

%==========================================================================
% (4) generate the decoder output from the optimal path
state_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);
end
decodeder_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)';
end
decoder_output=reshape(decoder_output_matrix,1,k*(depth_of_trellis-L+1));
cumulated_metric=state_metric(1,1);