編碼仿真之RM編譯碼實現

關於RM碼的詳細說明-> 德莉莎世界第一可愛

RM碼生成矩陣構造函數RMG代碼見文末

close all
clear all
clc

r=1;
m=5;
k=0;
for i=0:r
    k=k+nchoosek(m,i);
end
d=pow2(m-r);
t=fix((d-1)/2);
len=pow2(m);
%encode
G=RMG(r,m);
u=randBinary(k);
s='u:';
s=strcat(s,int2str(u));
disp(s)

c=mod(u*G,2);
s='code:';
s=strcat(s,int2str(c));
disp(s)
%error
err_num=randi(t);
s='error num:';
s=strcat(s,num2str(err_num));
disp(s)
E=zeros(1,len);
while err_num
    pos=randi(len);
    E(pos)=E(pos)+1;
    err_num=err_num-1;
end
E=mod(E,2);
s='error sample:';
s=strcat(s,int2str(E));
disp(s)
%decode
r=mod(c+E,2);
s='receive code:';
s=strcat(s,int2str(r));
disp(s)

H=[1 1;1 -1];
w=zeros(1,len);
for i=1:len
    w(i)=r(i)*2-1;
end
for i=1:m
    Him=kron(kron(eye(pow2(m-i)),H),eye(pow2(i-1)));
    w=w*Him;
end

max_pos=1;
for i=2:len
    if abs(w(max_pos))<abs(w(i))
        max_pos=i;
    end
end

message=zeros(1,k);
if w(max_pos)>0
    message(1)=1;
else
    message(1)=0;
end
max_pos=max_pos-1;
for i=2:k
    message(i)=mod(max_pos,2);
    max_pos=fix(max_pos/2);
end
s='message:';
s=strcat(s,int2str(message));
disp(s)

sc=message*G;
sr=mod(sc+r,2);
s='distance:';
s=strcat(s,num2str(sum(sr)));
disp(s)

RMG函數代碼

function [ G ] = RMG( r,m )
% 
%   RM碼生成矩陣
%   迭代構造

if r>m
    disp('check r and m');
    return;
end

len1=pow2(m);
if r==0
    G=zeros(1,len1);
    for i=1:len1
        G(i)=1;
    end
    return ;
end

if r==m
    z=zeros(1,len1);
    z(len1)=1;
    G=[RMG(r-1,m);z];
    return ;
end

len2=pow2(m-1);
tem=RMG(r,m-1);
sum=0;
for i=0:r-1
    sum=sum+nchoosek(m-1,i);
end
z=zeros(sum,len2);
G=[tem tem;z RMG(r-1,m-1)];


end