%file name: crcr.m
%Written by Dr. James S. Kang, Cal Poly Pomona.
%Calculate the remainder for the received data d and generator sequence g.
%d = received data such as [1 0 1 0 0 1 0 1] = data + CRC
%g = generator sequence such as [1 1 1 1 1].
%q = quotient sequence.
%r = remainder.
%To run the program, try
% >>crcr([1 0 1 0 0 1 0 1],[1 1 1 1 1])  <Enter>
function[r] = crcr(d,g)
nd=size(d,2); %nd = length of d.
ng=size(g,2); %ng = length of g.
fnzd=min(find(d)); %fnzd = index of first nonzero of d.
fnzg=min(find(g)); %fnzg = index of first nonzero of g.
ld=nd-fnzd+1; %ld = length of d from first nonzero.
s = sum(d);
g=g(1,fnzg:ng); %g starting from the first nonzero.
ng=size(g,2); %ng = length of g.
da=d(1,fnzd:nd); %da = data starting from the first nonzero.
nda=size(da,2); %b = all zero vector of length ng - 1.
fnzda=min(find(da)); %fnzda = index of the first nonzero of da.
nz=nda-ng; %nz = length of da minus the length of g.
b1=zeros(1,nz); %b1 = all zero vector of length nz.
v=[g,b1]; %v = g augmented by b1.
az=zeros(1,1);

if s >0

   nq=nda-ng+1; %nq = length of quotient.
   	for i = 1:nq
   	  if da(i) == 1
		q(i) = 1;
		da=[rem(da+v,2)]; %da = modulo 2 sum of da and v.
	  else
		q(i) = 0;
	  end
	  v=[az,v(1,1:nda-1)]; %v is shifted to the right by 1.	
	end
   	for i=1:ng-1
	  r(i) = da(1,nda-ng+1+i);
	end

else
	r=zeros(1,ng-1);
end
disp('The quotient = ')
disp(q)
disp('The remainder = ')
disp(r)
s = sum(r);
if s==0 disp('There is no error'); 
 else disp('There may be error(s)'); end