matlab卷积码程序

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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');