1、卷积码编码
function [output]=cnv_encd(input)
%output=cnv_encd(g,k0,input) 卷积码编码函数 %g 生成矩阵 %k0 输入码长
%input 输入信源序列 %output 输出卷积编码序列 g=[1 1 1;1 0 1];编码矩阵 k0=1;
input=[1 1 0 1];
if rem(length(input),k0)>0
input=[input,zeros(size(1:k0-rem(length(input),k0)))]; end
n=length(input)/k0;
if rem(size(g,2),k0)>0
error('Error,g is not of the right size.') end
li=size(g,2)/k0; n0=size(g,1);
u=[zeros(size(1:(li-1)*k0)),input,zeros(size(1:(li-1)*k0))];
u1=u(li*k0:-1:1); for i=1:n+li-2
u1=[u1,u((i+li)*k0:-1:i*k0+1)]; end
uu=reshape(u1,li*k0,n+li-1);
output=reshape(rem(g*uu,2),1,n0*(n+li-1));
2、Viterbi译码程序
1）
function y=bin2deci(x) l=length(x); y=(l-1:-1:0); y=2.^y; y=x*y'; 2）
function y=deci2bin(x,l) y=zeros(1,l);
i=1;
while x>=0 & i<=l y(i)=rem(x,2); x=(x-y(i))/2; i=i+1; end
y=y(l:-1:1); 3）
function distance=metric(x,y) if x==y
distance=0; else
distance=1; end 4）
function [next_state,memory_contents]=nxt_stat(current_state,input,L,k) binary_state=deci2bin(current_state,k*(L-1)); binary_input=deci2bin(input,k);
next_state_binary=[binary_input,binary_state(1:(L-2)*k)]; next_state=bin2deci(next_state_binary);
memory_contents=[binary_input,binary_state]; 5）
function [decoder_output,survivor_state,cumulated_metric]=viterbi(channel,snr_db)
G=[1 1 1;1 0 1]; % G 卷积编码矩阵，如（2,1,3)卷积码生成矩阵[1 1 1;1 0 1],可以根据自己的需要输入编码矩阵
k=1; % k 信息源输入端口数 k=1 channel=[1 1 0 1 0 1 0 0 1 0 1 1 ]; %信源编码
snr_db=6;%信噪比，可以通过调节信噪比大小观察viterbi译码的性能 %bpsk调制
channel_output=bpsk(channel,snr_db);%调用bpsk函数,得到信道编码
n=size(G,1); % n 编码输出端口数量,(2,1,3)中n=2 if rem(size(G,2),k)~=0 %当G列数不是k的整数倍时 error('Size of G and k do not agree') %发出出错信息 end
if rem(size(channel_output,2),n)~=0 %当输出量元素个数不是输出端口的整数倍时 error('channel output not of the right size') end
N=size(G,2)/k; %得出移位数，即寄存器的个数 M=2^k;
number_of_states=2^(k*(N-1)); %状态数
for j=0:number_of_states-1 %j表示当前寄存器组的状态因为状态是从零 %开始的,所以循环从0到number_of_states-1 for m=0:M-1 %m为从k个输入端的信号组成的状态，总的状 %态数为2^k，所以循环从0到2^k-1
% nxt_stat完成从当前的状态和输入的矢量得出下寄存器组的一个状态 [next_state,memory_contents]=nxt_stat(j,m,N,k);%调用nxt_stat函数 input(j+1,next_state+1)=m;
branch_output=rem(memory_contents*G',2); nextstate(j+1,m+1)=next_state;
output(j+1,m+1)=bin2deci(branch_output); end end % state_metric数组用于记录译码过程在每状态时的汉明距离 % state_metric大小为number_of_states 2，（:,1）当前 % 状态位置的汉明距离，为确定值，而（:,2）为当前状态加输入 % 得到的下一个状态汉明距离，为临时值 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); for i=1:depth_of_trellis-N+1
flag=zeros(1,number_of_states); if(i<=N)
step=2^(k*(N-i)); else
step=1; end
for j=0:step:number_of_states-1 for m=0:M-1
branch_metric=0;
binary_output=deci2bin(output(j+1,m+1),n); for ll=1:n
branch_metric=branch_metric+metric(channel_output_matrix(ll,i),binary_output(ll)); end % 选择码间距离较小的那条路径 % 选择方法： % 当下一个状态没有被访问时就直接赋值，否则，用比它小的将其覆盖
if(( state_metric(nextstate(j+1,m+1)+1,2)>state_metric(j+1,1)+branch_metric) | flag(nextstate(j+1,m+1)+1)==0 )
state_metric(nextstate(j+1,m+1)+1,2)=state_metric(j+1,1)+branch_metric; survivor_state(nextstate(j+1,m+1)+1,i+1)=j; flag(nextstate(j+1,m+1)+1)=1; end end end
state_metric=state_metric(:,2:-1:1); end
for i=depth_of_trellis-N+2:depth_of_trellis flag=zeros(1,number_of_states);
% 状态数从number_of_states→number_of_states/2→...→2→1 %程序说明同上，只不过输入矢量只为0
last_stop=number_of_states/(2^(k*(i-depth_of_trellis+N-2))); 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
% 从最佳路径中产生解码
% 译码过程可从数组survivor_state的最后一个位置向前逐级译码 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
decoder_output_matrix=zeros(k,depth_of_trellis-N+1); for i=1:depth_of_trellis-N+1
% 根据数组input的定义来得出从当前状态到下一个状态的输入信号矢量 dec_output_deci=input(state_sequence(1,i)+1,state_sequence(1,i+1)+1); dec_output_bin=deci2bin(dec_output_deci,k); % 将一次译码存入译码输出矩阵decoder_output_matrix相应的位置 decoder_output_matrix(:,i)=dec_output_bin(k:-1:1)'; end
decoder_output=reshape(decoder_output_matrix,1,k*(depth_of_trellis-N+1)); cumulated_metric=state_metric(1,1);
3、卷积码译码误码性能分析
clear all; clc;
cycl = 50;
snr_db = 0:1:10; % 输入信息
msg = randint(1,1024);
ber0 = zeros(cycl,length(snr_db)); ber1 = zeros(cycl,length(snr_db)); ber2 = zeros(cycl,length(snr_db));
% Trellises
trel = poly2trellis(3,[5 7]); Tfine trellis for rate 1/2 code. for n = 1:cycl
for x = 1:length(snr_db) % Code words
code = convenc(msg,trel); % Encode. % Interleaver state = 20;
inter = randintrlv(code,state); % BPSK 调制
s0 = sign(msg - 0.5); s1 = sign(inter-0.5); s2 = sign(code-0.5); % AWGN Channel
add_noise0=awgn(s0,snr_db(x),'measured'); add_noise1=awgn(s1,snr_db(x),'measured'); add_noise2=awgn(s2,snr_db(x),'measured'); % Deinterleaver with noise for soft decoding deinter_noise = randdeintrlv(add_noise1,state); % 解调
r_0 = 0.5*sign(add_noise0) + 0.5; r_1 = 0.5*sign(add_noise1) + 0.5; r_2 = 0.5*sign(add_noise2) + 0.5; % Deinterleaver
deinter_1 = randdeintrlv(r_1,state); % Traceback length tblen = 5;
% vitdec 硬判决
decoded1 = vitdec(deinter_1,trel,tblen,'cont','hard');
% vitdec 软判决
[y,qcode] = quantiz(deinter_noise,[-.75 -.5 -.25 0 .25 .5 .75],7:-1:0); decoded2 = vitdec(qcode,trel,tblen,'cont','soft',3); % 比较误码率
[num0,rat0] = biterr(r_0,msg);
[num1,rat1] = biterr(double(decoded1(tblen+1:end)),msg(1:end-tblen)); [num2,rat2] = biterr(double(decoded2(tblen+1:end)),msg(1:end-tblen)); ber0(n,x) = rat0; ber1(n,x) = rat1; ber2(n,x) = rat2; end end
ber0 = mean(ber0); ber1 = mean(ber1); ber2 = mean(ber2);
semilogy(snr_db,ber0,'b-o',snr_db,ber1,'r-s',snr_db,ber2,'k-p'); xlabel('SNR (dB)'); ylabel('BER');
legend('Uncoded','Hard Coded','Soft Coded');
title('Performance of convolutional code with rate 1/2');