jjma.m

用matlab实现卷积码的编码与解码过程

%survivor state是一个矩阵，它显T了通过网格的最优路径，这个矩阵通过一个单独
%的函数metric(x,y)给出。
%其中G是一个矩阵，它的何一行决定了从移位寄存器到输入码宇的连接方式.
%这里，我们做了一个简单的(2,1,6)卷积码编码器。
k=1;
G=[1 1 1 1 0 1;1 0 0 1 0 0]; 
input=[1 0 0 1 0 1];
figure;plot(input,'*r') %输入信号input
s=input;
g1=G(1,:);
g2=G(2,:);
c1=conv(s,g1);%作卷积
c2=conv(s,g2);
n=length(c1);
c=zeros(1,2*n);
for i=1:n
    c(2*i-1)=c1(i);c(2*i)=c2(i);
end
for i=1:2*n
    if(mod(c(i),2)==0)
        c(i)=0;
        else c(i)=1;
    end
end
output=c;
channel_output=output;
figure;plot(output,'*b') %输出的卷积码
n=size(G,1);
%检验G的维数
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('channle output not of the right size')
end
L=size(G,2)/k;
number_of_states=2^((L-1)*k);
%生状态转移矩阵，输出矩阵和输入矩阵
for j=0:number_of_states-1
  for t=0:2^k-1
    [next_state,memory_contents]=nxt_stat(j,t,L,k);
    input(j+1,next_state+1)=t;
    branch_output=rem(memory_contents*G',2);
    nextstate(j+1,t+1)=next_state;
    output(j+1,t+1)=bin2deci(branch_output);
  end
end
input;
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);
[row_survivor col_survivor]=size(survivor_state);
%开始非尾信道输出的解码
%i为段，j为何一阶段的状态，t为输入
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 t=0:2^k-1
        branch_metric=0;
        binary_output=deci2bin(output(j+1,t+1),n);
          for tt=1:n
branch_metric=branch_metric+metric(channel_output_matrix(tt,i),binary_output(tt));
end
if ((state_metric(nextstate(j+1,t+1)+1,2)>state_metric(j+1,1)+branch_metric)|flag(nextstate(j+1,t+1)+1)==0)
state_metric(nextstate(j+1,t+1)+1,2)=state_metric(j+1,1)+branch_metric;
                  survivor_state(nextstate(j+1,t+1)+1,i+1)=j;
                  flag(nextstate(j+1,t+1)+1)=1;
                  end
            end
end
state_metric=state_metric(:,2:-1:1);
end
%开始尾信道输出的解码
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 tt=1:n
branch_metric=branch_metric+metric(channel_output_matrix(tt,i),binary_output(tt));
            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
%从最优路径产生解码输出
%由段得到状态序列，再由状序列从input矩阵中得到该段的输出
state_sequence=zeros(1,depth_of_trellis+1);
size(state_sequence);
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
state_sequence;
decoder_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);
figure;plot(decoder_output,'*r') %还原出的输入信号