scripts init

scripts/commpy/channelcoding/algcode.py

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+
+
+# Authors: Veeresh Taranalli <veeresht@gmail.com>
+# License: BSD 3-Clause
+
+from fractions import gcd
+from numpy import array, arange, concatenate, convolve
+
+from commpy.channelcoding.gfields import GF, polymultiply, poly_to_string
+from commpy.utilities import dec2bitarray, bitarray2dec
+
+__all__ = ['cyclic_code_genpoly']
+
+def cyclic_code_genpoly(n, k):
+    """
+    Generate all possible generator polynomials for a (n, k)-cyclic code.
+
+    Parameters
+    ----------
+    n : int
+        Code blocklength of the cyclic code.
+
+    k : int
+        Information blocklength of the cyclic code.
+
+    Returns
+    -------
+    poly_list : 1D ndarray of ints
+        A list of generator polynomials (represented as integers) for the (n, k)-cyclic code.
+
+    """
+
+
+    if n%2 == 0:
+        raise ValueError("n cannot be an even number")
+
+    for m in arange(1, 18):
+        if (2**m-1)%n == 0:
+            break
+
+    x_gf = GF(arange(1, 2**m), m)
+    coset_fields = x_gf.cosets()
+
+    coset_leaders = array([])
+    minpol_degrees = array([])
+    for field in coset_fields:
+        coset_leaders = concatenate((coset_leaders, array([field.elements[0]])))
+        minpol_degrees = concatenate((minpol_degrees, array([len(field.elements)])))
+
+    y_gf = GF(coset_leaders, m)
+    minpol_list = y_gf.minpolys()
+    idx_list = arange(1, len(minpol_list))
+    poly_list = array([])
+
+    for i in range(1, 2**len(minpol_list)):
+        i_array = dec2bitarray(i, len(minpol_list))
+        subset_array = minpol_degrees[i_array == 1]
+        if int(subset_array.sum()) == (n-k):
+            poly_set = minpol_list[i_array == 1]
+            gpoly = 1
+            for poly in poly_set:
+                gpoly_array = dec2bitarray(gpoly, 2**m)
+                poly_array = dec2bitarray(poly, 2**m)
+                gpoly = bitarray2dec(convolve(gpoly_array, poly_array) % 2)
+            poly_list = concatenate((poly_list, array([gpoly])))
+
+    return poly_list.astype(int)
+
+
+if __name__ == "__main__":
+    genpolys = cyclic_code_genpoly(31, 21)
+    for poly in genpolys:
+        print(poly_to_string(poly))