def decoder_euclid(w, syndromes):
s_poly = _lstrip0(_np.concatenate((syndromes[::-1], [1])))
_, _, errloc_poly = gf.euclid(gf.polyshift([1], 2 * self.t + 1),
s_poly,
pm=self.pm,
max_deg=self.t + 1)
return errloc_poly
def decode(self, W, method='euclid'):
alpha = np.array([2], np.int)
curr_deg = alpha
alpha_list_t = [alpha[0]]
for i in range(2 * self.t - 1):
curr_deg = gf.prod(curr_deg, alpha, self.pm)
alpha_list_t.append(curr_deg[0])
alpha_list_n = alpha_list_t.copy()
for i in range(self.n - 2 * self.t):
curr_deg = gf.prod(curr_deg, alpha, self.pm)
alpha_list_n.append(curr_deg[0])
alpha_list_t = np.array(alpha_list_t)
alpha_list_n = np.array(alpha_list_n)
result = np.zeros(W.shape, np.int)
if method == 'pgz':
for row in range(W.shape[0]):
deg_list = gf.polyval(W[row], alpha_list_t, self.pm)
if np.all(deg_list == 0):
result[row] = W[row]
else:
curr_dim = self.t
while (curr_dim > 0):
A = np.zeros((curr_dim, curr_dim), np.int)
for i in range(curr_dim):
A[i] = deg_list[i:curr_dim + i]
b = deg_list[curr_dim:2 * curr_dim]
value = gf.linsolve(A, b, self.pm)
if value is not np.nan:
value = np.concatenate((value, np.ones(1, np.int)))
break
curr_dim -= 1
if curr_dim == 0:
result[row] = np.nan
else:
roots = gf.polyval(value, alpha_list_n, self.pm)
roots = np.nonzero(np.logical_not(roots))
err_pos = (roots[0]) % self.n
result[row] = W[row]
result[row, err_pos] = np.logical_not(
result[row, err_pos]).astype(np.int)
if np.any(
gf.polyval(result[row], alpha_list_t, self.pm)
!= 0):
result[row, :] = np.nan
elif method == 'euclid':
alpha_list_t = alpha_list_t[::-1]
for row in range(W.shape[0]):
S = gf.polyval(W[row], alpha_list_t, self.pm)
S = np.concatenate((S, np.ones(1, np.int)))
z = np.array([1] + [0 for x in range(2 * self.t + 1)], np.int)
r, A, Lambda = gf.euclid(z, S, self.pm, self.t)
roots = gf.polyval(Lambda, alpha_list_n, self.pm)
roots = np.nonzero(np.logical_not(roots))
err_pos = (roots[0]) % self.n
result[row] = W[row]
result[row, err_pos] = np.logical_not(
result[row, err_pos]).astype(np.int)
if np.any(gf.polyval(result[row], alpha_list_t, self.pm) != 0):
result[row, :] = np.nan
return result
def decode(self, W, method='euclid'):
num_of_message = W.shape[0]
answ = numpy.empty(W.shape, dtype=int)
double_t = 2 * self.t
for i in range(num_of_message):
if method == 'euclid':
syndrome_arr = gf.polyval(W[i], self.R, self.pm)
if not any(syndrome_arr):
answ[i] = W[i]
continue
syndrome_arr = numpy.hstack(
(syndrome_arr, numpy.array([1], dtype=int)))
z_in_pow_poly = numpy.zeros(double_t + 2, dtype=int)
z_in_pow_poly[0] = 1
zero_counter = 0
for x in syndrome_arr:
if x == 0:
zero_counter += 1
else:
break
Lambda = gf.euclid(z_in_pow_poly, syndrome_arr[zero_counter:],
self.pm, self.t)[2]
Lambda_pow = Lambda.shape[0] - 1
answ[i], num_of_root = self.correction(Lambda, W[i])
if Lambda_pow != num_of_root:
answ[i] = numpy.nan
#answ[i] = 2 Программы со сбором статистики, построением графиков, ожидают,
#что при отказах будет возвращаться строка двоек из-за проблем со сравнением numpy.nan находящегося в целочисленном массиве
continue
else:
syndrome_arr = gf.polyval(W[i], self.R_for_pgz, self.pm)
if not any(syndrome_arr):
answ[i] = W[i]
continue
arr = numpy.empty((self.t, self.t), dtype=int)
for k in range(self.t):
arr[k] = syndrome_arr[k:k + self.t]
b_arr = numpy.array(syndrome_arr[self.t:])
j = 0
while j != self.t:
Lambda = gf.linsolve(arr[:self.t - j, :self.t - j], b_arr,
self.pm)
if not numpy.array_equal(Lambda, Lambda):
j += 1
b_arr = syndrome_arr[self.t - j:2 * (self.t - j)]
else:
break
if j == self.t:
answ[i] = numpy.nan
#answ[i] = 2
continue
Lambda = numpy.hstack((Lambda, numpy.array([1])))
answ[i] = self.correction(Lambda, W[i])[0]
if any(gf.polyval(answ[i], self.R_for_pgz, self.pm)):
answ[i] = numpy.nan
#answ[i] = 2
return answ
def decode(self, W, method='euclid'):
message_number, n = W.shape
# res - результат
res = np.zeros(W.shape).astype('int')
# PGZ
for i in range(message_number):
# s - синдром
# для принятоо слова W вычислим синдром
s = gf.polyval(W[i, :], self.R, self.pm)
# если все s = 0, то возвращаем W в качестве ответа
if np.all(s == 0):
res[i] = W[i].copy()
continue
# вычислим коэффициенты полинома локаторов ошибок путем решения СЛАУ
if method == 'pgz':
for j in range(self.t, 0, -1):
# составим матрицу A для СЛАУ
A = np.zeros((j, j)).astype('int')
for k in range(j):
A[k, :] = s[k:k + j]
b = s[j:2 * j]
# решаем СЛАУ
Lambda = gf.linsolve(A, b, self.pm)
if not np.any(np.isnan(Lambda)):
break
if np.any(np.isnan(Lambda)):
res[i] = np.nan
continue
Lambda = np.append(Lambda, np.array([1]))
elif method == 'euclid':
s = np.append(s[::-1], np.array([1]))
# z^(2t + 1)
z = np.zeros(((self.R.size + 1) + 1), dtype=np.int)
z[0] = 1
# алгоритм евклида
# z^(2t + 1) * A(z) + S(z)L(z) = r(z)
# находим L(z)
Lambda = gf.euclid(z, s, self.pm, max_deg=self.t)[2]
# получаем позиции ошибок
roots = gf.polyval(Lambda, self.pm[:, 1], self.pm)
pos_error = np.nonzero(roots.reshape(-1) == 0)[0]
# инвертируем биты в позициях ошибок
tmp = W[i].copy()
tmp[pos_error] = 1 - tmp[pos_error].astype(np.int)
res[i] = tmp
s = gf.polyval(res[i].astype(int), self.R, self.pm)
if not np.all(s == 0):
res[i, :] = np.ones(self.n) * np.nan
continue
return res
def test_euclid():
pm = gf.gen_pow_matrix(37)
p1 = np.array([2, 14, 22, 23, 8, 17, 31, 11, 26, 3])
p2 = np.array([31, 23, 30, 31, 11, 9])
right_answer = (np.array([24, 8, 11]), np.array([1, 23, 14]),
np.array([19, 14, 2, 21, 7, 12, 11]))
max_deg = 2
result = gf.euclid(p1, p2, pm, max_deg=max_deg)
assert_equal(right_answer[0], result[0])
assert_equal(right_answer[1], result[1])
assert_equal(right_answer[2], result[2])
def EVCL(self, s):
arr = np.ones(s.shape[0] + 1)
for i in range(s.shape[0]):
arr[i] = s[s.shape[0] - i - 1]
arr2 = np.zeros(self.t * 2 + 2)
arr2[0] = 1
#print(arr, arr2, self.pm, self.t)
n = gf.euclid(arr, arr2, self.pm, self.t+1)
#print(n)
n = n[1]
return n
def decode(self, W, method='euclid'):
assert method == 'euclid' or method == 'pgz'
t = self.R.shape[0] // 2
n = W.shape[1]
is_nan = False
assert n == self.pm.shape[0]
res = np.zeros_like(W, dtype=object)
for i in range(W.shape[0]):
w = W[i]
s = gf.polyval(w, self.R, self.pm)
if (s == 0).all():
res[i] = w
continue
if method == 'euclid':
s = s[::-1]
z = np.zeros(2 * t + 2, dtype=np.int64)
z[0] = 1
s = np.concatenate((s, np.array([1])))
r, a, lam = gf.euclid(z, s, self.pm, max_deg=t)
else:
lam = np.nan
for errors in range(t, 0, -1):
A = [[s[k] for k in range(j, j + errors)]
for j in range(errors)]
A = np.array(A)
b = [s[k] for k in range(errors, errors * 2)]
b = np.array(b)
lam = gf.linsolve(A, b, self.pm)
if lam is not np.nan:
break
if lam is np.nan:
res[i] = np.nan
is_nan = True
continue
lam = np.concatenate((lam, np.array([1])))
values = gf.polyval(lam, self.pm[:, 1], self.pm)
num_roots = 0
#res[i] = w
for j in range(values.shape[0]):
if values[j] == 0:
root = self.pm[j, 1]
alpha = gf.divide(1, root, self.pm)
index = self.pm[alpha - 1, 0]
w[n - index - 1] = 1 - w[n - index - 1]
num_roots += 1
if num_roots != lam.shape[0] - 1:
res[i] = np.nan
is_nan = True
continue
res[i] = w
if not is_nan:
res = res.astype(np.int64)
return res
def decode(self, W, method='euclid'): V = W.astype(object) for i in range(len(V)): s = gf.polyval(V[i], self.R, self.pm) for j in s: if j != 0: break else: continue if method == 'pgz': e = s.size//2 while e > 0: S = np.empty((e,e),int) for j in range(e): S[j] = s[j:j+e] x = gf.linsolve(S,s[e:2*e],self.pm) if not np.any(np.isnan(x)): break e -= 1 else: V[i,:] = np.nan continue x = np.append(x, [1]) if method == 'euclid': S = np.append(s[::-1], [1]) x = np.zeros(s.size + 2,int) x[0] = 1 x = gf.euclid(x, S, self.pm, max_deg=s.size//2)[2] e = x.size - 1 x = gf.polyval(x, self.pm[:,1], self.pm) x = self.pm[np.flatnonzero(x==0), 1] if method == 'euclid' and x.size != e: V[i,:] = np.nan continue x = self.pm[x-1,0] - 1 V[i,x] = V[i,x]^1 if method == 'pgz': s = gf.polyval(V[i], self.R, self.pm) for j in s: if j != 0: V[i,:] = np.nan break return V
def decode(self, w, method='euclid'):
f = open(method + '.txt', 'a')
u = np.zeros((w.shape[0], w.shape[1]), int)
for i in range(w.shape[0]):
s = gf.polyval(w[i], self.R, self.pm)
if np.count_nonzero(s) == 0:
u[i] = w[i]
continue
if method == 'pgz':
t = time.clock()
A, b = build_m(s, self.t)
L = gf.linsolve(A, b, self.pm)
step = self.t - 1
while type(L) == type(np.nan) and step > 0:
A, b = build_m(s, step)
L = gf.linsolve(A, b, self.pm)
step -= 1
if type(L) == type(np.nan):
u[i] = -1
continue
L = np.concatenate((L, [1]))
t = time.clock() - t
if method == 'euclid':
t = time.clock()
s = np.concatenate((s[::-1], [1]))
z = np.zeros(2 * self.t + 2, int)
z[0] = 1
L = gf.euclid(z, s, self.pm, self.t)[2]
t = time.clock() - t
f.write(str(t) + '\n')
val = gf.polyval(L, self.pm[:, 1].reshape((self.pm.shape[0])),
self.pm)
pos = []
for a in range(val.size):
if val[a] == 0:
pos.append(a)
if len(pos) != L.size - 1:
u[i] = -1
continue
u[i] = w[i]
for j in pos:
u[i, j] = (u[i, j] + 1) % 2
f.close()
return u
def decoding(W, R, pm, method='euclid'):
n_mes = W.shape[0]
n = W.shape[1]
V = np.zeros((n_mes, n))
t = int(R.size / 2)
for mes_idx in range(n_mes):
# Step 1. Computing syndrome polynomials:
s = gf.polyval(W[mes_idx, :], R, pm)
if np.count_nonzero(s) == 0:
V[mes_idx, :] = W[mes_idx, :]
continue
# Step 2. Computing Lambda(z) coefficients:
# PGZ decoder:
if method == 'pgz':
for nu in range(t, 0, -1):
A = hankel(s[:nu], s[(nu - 1):(2 * nu - 1)])
b = s[nu:(2 * nu)]
x = gf.linsolve(A, b, pm)
if np.all(np.isnan(x) == False):
break
if np.any(np.isnan(x) == True):
W[mes_idx, :] = np.nan
continue
Lambda = np.append(x, [1])
# Euclid decoder:
elif method == 'euclid':
S = np.append(s[::-1], [1])
z_pow_d = np.zeros((2 * t + 2), dtype=int)
z_pow_d[0] = 1
Lambda = gf.euclid(z_pow_d, S, pm, max_deg=t)[2]
else:
raise ValueError("Unknown method name")
# Step 3 and 4. Finding all roots of Lambda(z) and
# Computing error positions:
error_positions = np.where(gf.polyval(Lambda, pm[:, 1], pm) == 0)[0]
# Step 5. Computing decoded message:
v = W[mes_idx, :].copy()
v[error_positions] = np.abs(v[error_positions] - 1)
# Step 6. Checking decoded message:
if np.count_nonzero(gf.polyval(v, R, pm)) == 0:
V[mes_idx, :] = v.copy()
else:
V[mes_idx, :] = np.nan
return V
def decode(self, W, method='euclid'):
result = np.empty(W.shape)
for index, w in enumerate(W):
result[index] = w
s = gf.polyval(w, self.R, self.pm)
if np.all(s == 0):
continue
if method == 'euclid':
s = np.hstack((s[::-1], np.array([1], int)))
i = 0
while s[i] == 0:
i += 1
loc = gf.euclid(
np.hstack((np.array([1],
int), np.zeros(self.R.size + 1, int))),
s[i:], self.pm, self.R.size >> 1)[2]
else:
t = self.R.size >> 1
A = np.empty((t, t), int)
for i in range(t):
A[i] = s[i:i + t]
for v in range(t, 0, -1):
loc = gf.linsolve(A[:v, :v], s[v:2 * v], self.pm)
if np.array_equal(loc, loc):
loc = np.hstack((loc, np.array([1], int)))
break
if not np.array_equal(loc, loc):
result[index].fill(np.nan)
continue
roots_count = 0
for i, val in enumerate(self.pm[:, 1]):
if gf.polyval(loc, val.reshape(1), self.pm)[0] == 0:
roots_count += 1
result[index][i] = int(result[index][i]) ^ 1
if method == 'euclid' and roots_count != loc.size - 1:
result[index].fill(np.nan)
elif method == 'pgz':
s = gf.polyval(result[index].astype(int), self.R, self.pm)
if np.any(s != 0):
result[index].fill(np.nan)
return result
def _decode(self, w, method):
t = self.R.shape[0] // 2
syndromes = gf.polyval(w, self.R, self.pm)
if np.sum(syndromes != 0) == 0:
return w
if method == 'pgz':
lambda_ = np.nan
for nu in range(t, 0, -1):
a = np.array([[syndromes[j] for j in range(i, nu + i)]
for i in range(nu)],
dtype=np.int)
b = np.array([syndromes[i] for i in range(nu, 2 * nu)],
dtype=np.int)
lambda_ = gf.linsolve(a, b, self.pm)
if lambda_ is not np.nan:
break
if lambda_ is np.nan:
return np.full(self.n, np.nan, dtype=np.int)
lambda_ = np.concatenate([lambda_, [1]])
elif method == 'euclid':
z = np.zeros([2 * t + 2], dtype=np.int)
z[0] = 1
syndromic_polynom = np.concatenate([syndromes[::-1], [1]])
_, _, lambda_ = gf.euclid(z, syndromic_polynom, self.pm, max_deg=t)
else:
raise ValueError
n_roots = 0
locators_values = gf.polyval(lambda_, np.arange(1, self.n + 1),
self.pm)
for idx in range(1, self.n + 1):
if not locators_values[idx - 1]:
position = self.n - self.pm[gf.divide(1, idx, self.pm) - 1,
0] - 1
w[position] = 1 - w[position]
n_roots += 1
if n_roots != lambda_.shape[0] - 1:
return np.full(self.n, np.nan, dtype=np.int)
return w
def decode(self, W, method="euclid"):
"""Декодирование БЧХ"""
fi = []
for w in W:
synd = polyval(w, self.R, self.pm)
t = 0
for i in synd:
if i != 0:
t = -1
break
if t == 0:
fi.append(w)
continue
if method == "pgz":
v = self.t
while v > 0:
synd_m = np.empty([v, v], dtype=int)
for i in range(synd_m.shape[0]):
for j in range(synd_m.shape[1]):
synd_m[i][j] = synd[i + j]
synd_b = np.empty([v], dtype=int)
for i in range(synd_b.shape[0]):
synd_b[i] = synd[v + i]
L = linsolve(synd_m, synd_b, self.pm)
if np.isnan(L[0]):
v -= 1
continue
L = np.hstack([L, np.asarray(1)])
L_roots = set()
for i in range(self.pm.shape[0]):
x = polyval(L, np.asarray([self.pm[i][1]]), self.pm)
if (x[0] == 0):
L_roots.add(self.pm[i][1])
for i in L_roots:
j = self.pm[i - 1][0]
w[j - 1] ^= 1
synd = polyval(w, self.R, self.pm)
t = 0
for i in synd:
if i != 0:
t = -1
break
if t == 0:
fi.append(w)
break
else:
fi.append(np.nan)
break
if v == 0:
fi.append(np.nan)
else:
synd = np.concatenate((np.flip(synd), np.asarray([1])))
x = np.concatenate((np.asarray([1]), np.zeros(2 * self.t + 1, dtype=int)))
a, b, L = euclid(x, synd, self.pm, self.t)
L_roots = set()
for i in range(self.pm.shape[0]):
x = polyval(L, np.asarray([self.pm[i][1]]), self.pm)
if x[0] == 0:
L_roots.add(self.pm[i][1])
power = L.size - 1
i = 0
while L[i] == 0:
power -= 1
i += 1
if len(L_roots) != power: # количество корней не совпадает
fi.append(np.nan)
continue
for i in L_roots:
j = self.pm[i - 1][0]
w[j - 1] ^= 1
synd = polyval(w, self.R, self.pm)
t = 0
for i in synd:
if i != 0:
t = -1
break
if t == 0:
fi.append(w)
continue
else:
fi.append(np.nan)
continue
return np.asarray(fi)
def decode(self, W, method='euclid'):
sindrom = np.zeros((W.shape[0], 2*self.t)).astype('int')
V_hat = np.zeros((W.shape)).astype('int')
error = []
for i in range(W.shape[0]):
sindrom[i, :] = gf.polyval(W[i, :], self.R, self.pm)
if np.all(sindrom[i, :] == 0):
V_hat[i, :] = W[i, :]
else:
error.append(i)
for i in error:
if method == 'euclid':
# sindrom polynom
sindrom_poly = np.zeros(2*self.t + 1).astype('int')
s = sindrom[i, :]
s = s[::-1]
sindrom_poly[: -1] = s
sindrom_poly[-1] = 1
# z^(2t + 1)
z = np.zeros(2*self.t + 2).astype('int')
z[0] = 1
#euclid algorithm
r, A, loc_poly_coef = gf.euclid(z, sindrom_poly,
self.pm, max_deg=self.t)
elif method == 'pgz':
s = sindrom[i, :]
for errors_n in range(self.t, 0, -1):
# matrix for linear solve
S = np.zeros((errors_n, errors_n)).astype('int')
for j in range(errors_n):
S[j, :] = s[j: j + errors_n]
b = s[errors_n: 2 * errors_n]
lambda_ = gf.linsolve(S, b,self.pm)
if np.all(np.isnan(lambda_)):
continue
else:
break
# decode error
if (errors_n == 1) and np.all(np.isnan(lambda_)):
V_hat[i, :] = np.ones(self.n) * np.nan
continue
# coef of locator polynoms
loc_poly_coef = np.zeros(lambda_.shape[0] + 1).astype('int')
loc_poly_coef[-1] = 1
loc_poly_coef[: -1] = lambda_
# find root
locator_val = gf.polyval(loc_poly_coef, self.pm[:, 1], self.pm)
roots = self.pm[np.where(locator_val == 0)[0], 1]
pos_error = (-self.pm[roots - 1, 0]) % self.pm.shape[0]
pos_error = self.n - pos_error - 1
#error polynom
error_poly = np.zeros(self.n).astype('int')
error_poly[pos_error] = 1
#decode
v_hat = W[i, :] ^ error_poly
s_v_hat = gf.polyval(v_hat, self.R, self.pm)
if not np.all(s_v_hat == 0):
V_hat[i, :] = np.ones(self.n) * np.nan
continue
if (roots.shape[0] != loc_poly_coef.shape[0] - 1):
V_hat[i, :] = np.ones(self.n) * np.nan
continue
V_hat[i, :] = v_hat
return V_hat