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cyclgen.cc    281 lines (253 with data), 7.6 kB

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//Copyright (C) 2003 David Bateman
//
// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 3 of the
// License, or (at your option) any later version.
//
// This program is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program; if not, see
// <http://www.gnu.org/licenses/>.
//
// In addition to the terms of the GPL, you are permitted to link this
// program with any Open Source program, as defined by the Open Source
// Initiative (www.opensource.org)
#include <iostream>
#include <iomanip>
#include <sstream>
#include <octave/oct.h>
#include <octave/pager.h>
// A simplified version of the filter function for specific lengths of a and b
// in the Galois field GF(2)
Array<int>
filter_gf2 (const Array<int>& b, const Array<int>& a,
const Array<int>& x, const int& n)
{
int x_len = x.length ();
Array<int> si (dim_vector (n, 1), 0);
Array<int> y (dim_vector (x_len, 1), 0);
for (int i = 0; i < x_len; i++)
{
y(i) = si(0);
if (b(0) && x(i))
y(i) ^= 1;
for (int j = 0; j < n - 1; j++)
{
si(j) = si(j+1);
if (a(j+1) && y(i))
si(j) ^= 1;
if (b(j+1) && x(i))
si(j) ^= 1;
}
si(n-1) = 0;
if (a(n) && y(i))
si(n-1) ^= 1;
if (b(n) && x(i))
si(n-1) ^= 1;
}
return y;
}
// Cyclic polynomial is irreducible. I.E. it divides into x^n-1
// without remainder There must surely be an easier way of doing this
// as the polynomials are over GF(2).
static bool
do_is_cyclic_polynomial (const Array<int>& a, const int& n, const int& m)
{
Array<int> y (dim_vector (n+1, 1), 0);
Array<int> x (dim_vector (n-m+2, 1), 0);
y(0) = 1;
y(n) = 1;
x(0) = 1;
Array<int> b = filter_gf2 (y, a, x, n);
b.resize (dim_vector (n+1, 1), 0);
Array<int> p (dim_vector (m+1, 1), 0);
p(0) = 1;
Array<int> q = filter_gf2 (a, p, b, m);
for (int i = 0; i < n+1; i++)
if (y(i) ^ q(i))
return false;
return true;
}
DEFUN_DLD (cyclgen, args, nargout,
"-*- texinfo -*-\n\
@deftypefn {Loadable Function} {@var{h} =} cyclgen (@var{n}, @var{p})\n\
@deftypefnx {Loadable Function} {@var{h} =} cyclgen (@var{n}, @var{p}, @var{typ})\n\
@deftypefnx {Loadable Function} {[@var{h}, @var{g}] =} cyclgen (@dots{})\n\
@deftypefnx {Loadable Function} {[@var{h}, @var{g}, @var{k}] =} cyclgen (@dots{})\n\
Produce the parity check and generator matrix of a cyclic code. The parity\n\
check matrix is returned as a @var{m} by @var{n} matrix, representing the\n\
[@var{n},@var{k}] cyclic code. @var{m} is the order of the generator\n\
polynomial @var{p} and the message length @var{k} is given by\n\
@code{@var{n} - @var{m}}.\n\
\n\
The generator polynomial can either be a vector of ones and zeros,\n\
and length @var{m} representing,\n\
@tex\n\
$$ p_0 + p_1 x + p_2 x^2 + \\cdots + p_m x^{m-1} $$\n\
@end tex\n\
@ifnottex\n\
\n\
@example\n\
@var{p}(1) + @var{p}(2) * x + @var{p}(3) * x^2 + ... + @var{p}(@var{m}) * x^(m-1)\n\
@end example\n\
@end ifnottex\n\
\n\
The terms of the polynomial are stored least-significant term first.\n\
Alternatively, @var{p} can be an integer representation of the same\n\
polynomial.\n\
\n\
The form of the parity check matrix is determined by @var{typ}. If\n\
@var{typ} is 'system', a systematic parity check matrix is produced. If\n\
@var{typ} is 'nosys' and non-systematic parity check matrix is produced.\n\
\n\
If requested @code{cyclgen} also returns the @var{k} by @var{n} generator\n\
matrix @var{g}.\
\n\
@seealso{hammgen, gen2par, cyclpoly}\n\
@end deftypefn")
{
octave_value_list retval;
int nargin = args.length ();
unsigned long long p = 0;
int n, m, k, mm;
bool system = true;
Array<int> pp;
if (nargin < 2 || nargin > 3)
{
print_usage ();
return retval;
}
n = args(0).int_value ();
m = 1;
while (n > (1<<(m+1)))
m++;
pp.resize (dim_vector (n+1, 1), 0);
if (args(1).is_scalar_type ())
{
p = (unsigned long long)(args(1).int_value ());
mm = 1;
while (p > ((unsigned long long)1<<(mm+1)))
mm++;
for (int i = 0; i < mm+1; i++)
pp(i) = (p & (1<<i) ? 1 : 0);
}
else
{
Matrix tmp = args(1).matrix_value ();
if ((tmp.rows () != 1) && (tmp.columns () != 1))
{
error ("cyclgen: generator polynomial must be a vector");
return retval;
}
if (tmp.rows () == 1)
{
mm = tmp.columns ();
for (int j = 0; j < mm; j++) {
if (tmp(0, j) == 1) {
p |= ((unsigned long long)1 << j);
pp(j) = 1;
}
else if (tmp(0, j) != 0) {
error ("cyclgen: illegal generator polynomial");
return retval;
}
}
}
else
{
mm = tmp.rows ();
for (int i = 0; i < mm; i++)
{
if (tmp(i, 0) == 1)
{
p |= ((unsigned long long)1 << i);
pp(i) = 1;
}
else if (tmp(i, 0) != 0)
{
error ("cyclgen: illegal generator polynomial");
return retval;
}
}
}
mm = mm - 1;
}
k = n - mm;
if (nargin > 2)
{
if (args(2).is_string ())
{
std::string s_arg = args(2).string_value ();
if (s_arg == "system")
system = true;
else if (s_arg == "nosys")
system = false;
else
{
error ("cyclgen: illegal argument");
return retval;
}
}
else
{
error ("cyclgen: illegal argument");
return retval;
}
}
// Haven't implemented this since I'm not sure what matlab wants here
if (!system)
{
error ("cyclgen: non-systematic generator matrices not implemented");
return retval;
}
if (!do_is_cyclic_polynomial (pp, n, mm))
{
error ("cyclgen: generator polynomial does not produce cyclic code");
return retval;
}
unsigned long long mask = 1;
unsigned long long *alpha_to =
(unsigned long long *)malloc (sizeof (unsigned long long) * n);
for (int i = 0; i < n; i++)
{
alpha_to[i] = mask;
mask <<= 1;
if (mask & ((unsigned long long)1<<mm))
mask ^= p;
}
Matrix parity (mm, n, 0);
for (int i = 0; i < n; i++)
for (int j = 0; j < mm; j++)
if (alpha_to[i] & ((unsigned long long)1<<j))
parity(j, i) = 1;
free (alpha_to);
retval(0) = octave_value (parity);
if (nargout > 1)
{
Matrix generator (k, n, 0);
for (int i = 0; i < (int)k; i++)
for (int j = 0; j < (int)mm; j++)
generator(i, j) = parity(j, i+mm);
for (int i = 0; i < (int)k; i++)
generator(i, i+mm) = 1;
retval(1) = octave_value (generator);
retval(2) = octave_value ((double)k);
}
return retval;
}
/*
%% Test input validation
%!error cyclgen ()
%!error cyclgen (1)
%!error cyclgen (1, 2, 3, 4)
*/
/*
;;; Local Variables: ***
;;; mode: C++ ***
;;; End: ***
*/