def rect_parity(codeword,nrows,ncols):
# construct rectangle
rectangle = []
for row in range(nrows):
rectangle.append(codeword[row*ncols:row*ncols+ncols])
# add row parity bits
row = 0
for row_parity_bit in codeword[nrows*ncols:nrows*ncols+nrows]:
rectangle[row].append(row_parity_bit)
row += 1
# add column parity bits
rectangle.append(codeword[nrows*ncols+nrows:])
# calculate parity
rows_with_error = []
cols_with_error = []
# row parity
for row in range(nrows):
if not PS2_tests.even_parity(rectangle[row][:ncols+1]):
rows_with_error.append(row)
# column parity
for col in range(ncols):
if not PS2_tests.even_parity([rectangle[row][col] for row in range(nrows+1)]):
cols_with_error.append(col)
# correct errors
if len(rows_with_error) == 1 and len(cols_with_error) == 1:
row = rows_with_error[0]
col = cols_with_error[0]
rectangle[row][col] = int(not rectangle[row][col]) # flip bit
# return the corrected data
message_sequence = []
for row in range(nrows):
for col in range(ncols):
message_sequence.append(rectangle[row][col])
return message_sequence
for j in xrange(nrows):
parity_bit = get_parity_bit(codeword, 'row', j)
row = get_row(codeword, j)
if is_error(row, parity_bit):
corrected_row = []
for i in xrange(ncols):
col = get_col(codeword, i)
parity_bit = get_parity_bit(codeword, 'col', i)
if is_error(col, parity_bit):
if corrected: return codeword[:nrows * ncols];
corrected_row.append(int(not row[i]))
corrected = True
else:
corrected_row.append(row[i])
corrected_code.extend(corrected_row)
else:
corrected_code.extend(row)
# for i in xrange(ncols):
# col = get_col(codeword, i)
# parity_bit = get_parity_bit(codeword, 'col', i)
# if is_error(col, parity_bit):
# corrected_col = []
# for j in xrange(nrows):
# row = get_row(codeword, j)
# parity_bit = get_parity_bit(codeword, 'row', j)
return corrected_code
if __name__ == '__main__':
PS2_tests.test_correct_errors(rect_parity)
return codeword[:k]
def compute_all_syndrome_results(h_matrix, n):
results = []
for i in xrange(n):
new_array = [0 for j in xrange(n)]
new_array[i] = 1
error_vector = array(new_array)
error_vector.shape = n,1
results.append(mod2(h_matrix*error_vector))
return results
if __name__ == '__main__':
# (7,4,3) Hamming code
G1 = matrix('1 0 0 0 1 1 0; 0 1 0 0 1 0 1; 0 0 1 0 0 1 1; 0 0 0 1 1 1 1',
dtype=int)
PS2_tests.test_linear_sec(syndrome_decode, 7, 4, G1)
# (8,4,3) rectangular parity code
G2 = matrix('1 0 0 0 1 0 1 0; 0 1 0 0 1 0 0 1; 0 0 1 0 0 1 1 0; 0 0 0 1 0 1 0 1', dtype=int)
PS2_tests.test_linear_sec(syndrome_decode, 8, 4, G2)
# (6,3,3) pairwise parity code
G3 = matrix('1 0 0 1 1 0; 0 1 0 0 1 1; 0 0 1 1 0 1', dtype=int)
PS2_tests.test_linear_sec(syndrome_decode, 6, 3, G3)
# (15,11,3) Hamming code
G4 = matrix('1 0 0 0 0 0 0 0 0 0 0 0 1 1 1; 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1; 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1; 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0; 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1; 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0; 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0; 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1; 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0; 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1; 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1')
PS2_tests.test_linear_sec(syndrome_decode, 15, 11, G4)
# template for 6.02 rectangular parity decoding using error triangulation
import PS2_tests
import numpy
def rect_parity(codeword,nrows,ncols):
counter = 0
row_sums = [0 for i in xrange(nrows)]
column_sums = [0 for i in xrange(ncols)]
for i in xrange(nrows):
for j in xrange(ncols):
row_sums[i] += codeword[counter]
column_sums[j] += codeword[counter]
counter += 1
row_errors = []
column_errors = []
broken_bits = 0
for i in xrange(nrows):
if (row_sums[i] % 2) != codeword[nrows*ncols+i]:
row_errors.append(i)
for j in xrange(ncols):
if (column_sums[j] % 2) != codeword[nrows*ncols+nrows+j]:
column_errors.append(j)
result = [codeword[k] for k in xrange(len(codeword)) if k <= (nrows*ncols-1)]
if len(row_errors) == 1 and len(column_errors) == 1:
result[row_errors[0]*ncols+column_errors[0]] = (result[row_errors[0]*ncols+column_errors[0]] + 1) % 2
return result
if __name__ == '__main__':
PS2_tests.test_correct_errors(rect_parity)
c = mod2(H * matrix(codeword).transpose())
if not equal(c, zeros((n - k, 1), int)):
for i in range(k):
if equal(c, syndromes[i]):
codeword[i] = int(not codeword[i]) # flip bit
break
return codeword[:k]
if __name__ == '__main__':
# (7,4,3) Hamming code
G1 = matrix('1 0 0 0 1 1 0; 0 1 0 0 1 0 1; 0 0 1 0 0 1 1; 0 0 0 1 1 1 1',
dtype=int)
PS2_tests.test_linear_sec(syndrome_decode, 7, 4, G1)
# (8,4,3) rectangular parity code
G2 = matrix(
'1 0 0 0 1 0 1 0; 0 1 0 0 1 0 0 1; 0 0 1 0 0 1 1 0; 0 0 0 1 0 1 0 1',
dtype=int)
PS2_tests.test_linear_sec(syndrome_decode, 8, 4, G2)
# (6,3,3) pairwise parity code
G3 = matrix('1 0 0 1 1 0; 0 1 0 0 1 1; 0 0 1 1 0 1', dtype=int)
PS2_tests.test_linear_sec(syndrome_decode, 6, 3, G3)
# (15,11,3) Hamming code
G4 = matrix(
'1 0 0 0 0 0 0 0 0 0 0 0 1 1 1; 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1; 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1; 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0; 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1; 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0; 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0; 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1; 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0; 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1; 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1'
)
