gen_h_bit.m

binary image expansion of parity check matrix for RS codes

%function H_bit=gen_H_bit(n,k,m)
%this matrix is used to precomputer generate matrix for rs(n,k) code 
%**************  parameter **************
m=4;
k=7;
n=15;
demo=1;
t2=n-k;
prim_poly=primpoly(m);
%**************  start  ******************

%*** generator of parity check matrix on symbol-level ***
H_sym=gf(zeros(t2-1,n),m);
a=gf(2,m);
rom=[2,4,8,3,6,12,11,5,10,7,14,15,13,9,0];
for i=1:t2
  xi=a^i;
  for j=0:n-1
      H_sym(i,j+1)=xi^(n-1-j);%in order of descending powers
  end;
end;

%*** generator of parity check matrix on bit-level ***
prim_poly_bit=de2bi(prim_poly,m+1,'left-msb');
prim_mat=gf(zeros(m,m),m);
prim_mat(1,:)=prim_poly_bit(1,2:m+1);
for i=2:m
    prim_mat(i,i-1)=1;
end;

H_bit=gf(zeros(t2*m,n*m),m);
H_sym_double=double(H_sym.x);
H_ele_mat=gf(zeros(m,m),m);
for i=1:t2
   for j=1:n
     H_ele_bit=de2bi(H_sym_double(i,j),m,'left-msb');
     for ii=1:m
       H_ele_mat=H_ele_mat+H_ele_bit(m-ii+1)*prim_mat^(ii-1);
       %H_ele_mat=H_ele_mat+H_ele_bit(ii)*prim_mat^(ii-1);
     end;
     H_bit((i-1)*m+1:i*m,(j-1)*m+1:j*m)=H_ele_mat';
     H_ele_mat=gf(zeros(m,m),m);
   end;
end;

%**************  test  ************
%**************  test on symbol level  ************
%a=gf([5 1 3 4 2],m);%test code polynomial in order of descending powers
msg=gf(randint(1,k,2^m),m)
codeword=rsenc(msg,n,k);
Dc=codeword*H_sym';
save('H_sym_out','H_sym');

%**************  test on bit level  ************
ad=double(codeword.x);
a_mat=de2bi(ad,m,'left-msb');
a_bit=gf(zeros(1,n*m),m);
for i=1:n
  a_bit(1,(i-1)*m+1:i*m)=gf(a_mat(i,:),m);
end;
Dcb=a_bit*H_bit';
FC=isempty(find(double(Dcb.x)));

if(demo) msg,codeword,H_sym,Dc,H_bit,Dcb,FC,end;