res = Mat(({0, 1, 2, 3, 4, 5, 6},S.D[1]), {})
for i in res.D[1]:
e = find_error(S[i]) # S[i] returns i-th column of S
for j in res.D[0]:
res[j,i] = e[j]
return res
## Task 8
s = "I'm trying to free your mind, Neo. But I can only show you the door. You're the one that has to walk through it."
P = bits2mat(str2bits(s)) # p[i] column is 4-bit nibble
## Ungraded task
# Use noise(A, s) to produce the transmitted message
# input: P - matrix being transmitted
print("Message w/o encoding and ecc:", bits2str(mat2bits(P + noise(P, 0.02))).encode("utf-8"))
## Task 9
C = G*P # encode
bits_before = len(str2bits(s)) # bits before encoding
bits_after = bits_before//4*7 # bits after encoding
print(bits_before, bits_after)
## Ungraded Task
CTILDE = C + noise(C, 0.02) # encoded message received
print("Message with encoding, but w/o ecc:", bits2str(mat2bits(R*CTILDE)).encode("utf-8"))
## Task 10
def correct(A):
"""
print(P)
## Task 9
C = G * P
print(C)
bits_before = len(str2bits(s))
print(bits_before)
bits_after = len(mat2bits(C))
print(bits_after
)
## Ungraded Task
CTILDE = C + noise(C, 0.02)
print(CTILDE)
## Task 10
def correct(A):
"""
Input: a matrix A each column of which differs from a codeword in at most one bit
Output: a matrix whose columns are the corresponding valid codewords.
Example:
>>> A = Mat(({0,1,2,3,4,5,6}, {1,2,3}), {(0,3):one, (2, 1): one, (5, 2):one, (5,3):one, (0,2): one})
>>> correct(A) == Mat(({0, 1, 2, 3, 4, 5, 6}, {1, 2, 3}), {(0, 1): 0, (1, 2): 0, (3, 2): 0, (1, 3): 0, (3, 3): 0, (5, 2): one, (6, 1): 0, (3, 1): 0, (2, 1): 0, (0, 2): one, (6, 3): one, (4, 2): 0, (6, 2): one, (2, 3): 0, (4, 3): 0, (2, 2): 0, (5, 1): 0, (0, 3): one, (4, 1): 0, (1, 1): 0, (5, 3): one})
True
"""
return A + find_error_matrix(H * A)
print(bits2str(mat2bits(CTILDE)))
print(bits2str(mat2bits(R * correct(CTILDE))))
def error_test(s, prob):
msg = bits2mat(str2bits(s))
cw = G*msg
rcvd = cw + noise(cw, prob)
msg_rcvd = R*correct(rcvd)
return s == bits2str(mat2bits(msg_rcvd))
Output: a matrix whose cth column is the error corresponding to the cth column of S.
Example:
>>> S = listlist2mat([[0,one,one,one],[0,one,0,0],[0,0,0,one]])
>>> find_error_matrix(S) == Mat(({0, 1, 2, 3, 4, 5, 6}, {0, 1, 2, 3}), {(1, 3): 0, (3, 0): 0, (2, 1): 0, (6, 2): 0, (5, 1): one, (0, 3): 0, (4, 0): 0, (1, 2): 0, (3, 3): 0, (6, 3): 0, (5, 0): 0, (2, 2): 0, (4, 1): 0, (1, 1): 0, (3, 2): one, (0, 0): 0, (6, 0): 0, (2, 3): 0, (4, 2): 0, (1, 0): 0, (5, 3): 0, (0, 1): 0, (6, 1): 0, (3, 1): 0, (2, 0): 0, (4, 3): one, (5, 2): 0, (0, 2): 0})
True
"""
return coldict2mat(
dict((k, find_error(c)) for (k, c) in mat2coldict(S).items()))
## Task 8
s = "I'm trying to free your mind, Neo. But I can only show you the door. You're the one that has to walk through it."
P = bits2mat(str2bits(s))
EP = P + noise(P, 0.02)
s_break = bits2str(mat2bits(EP))
# print(s_break)
## Task 9
C = G * P
bits_before = len(str2bits(s))
bits_after = len(mat2bits(C))
# print(bits_before, bits_after)
## Ungraded Task
CTILDE = C + noise(C, 0.04)
# print(bits2str(mat2bits(R * CTILDE)))
## Task 10
bits_before = len(mat2bits(P))
bits_after = len(mat2bits(C))
## Ungraded Task
CTILDE = C + noise(C, 0.02)
## Task 8
def correct(A):
"""
Input: a matrix A each column of which differs from a codeword in at most one bit
Output: a matrix whose columns are the corresponding valid codewords.
Example:
>>> A = Mat(({0,1,2,3,4,5,6}, {1,2,3}), {(0,3):one, (2, 1): one, (5, 2):one, (5,3):one, (0,2): one})
>>> correct(A)
Mat(({0, 1, 2, 3, 4, 5, 6}, {1, 2, 3}), {(0, 1): 0, (1, 2): 0, (3, 2): 0, (1, 3): 0, (3, 3): 0, (5, 2): one, (6, 1): 0, (3, 1): 0, (2, 1): 0, (0, 2): one, (6, 3): one, (4, 2): 0, (6, 2): one, (2, 3): 0, (4, 3): 0, (2, 2): 0, (5, 1): 0, (0, 3): one, (4, 1): 0, (1, 1): 0, (5, 3): one})
"""
return A + find_error_matrix(H * A)
if __name__ == '__main__':
import sys
ctilde = C + noise(C, float(sys.argv[2]))
s2 = bits2str(mat2bits(R * correct(ctilde)))
if s2 == s:
print('Fine')
else:
print('Failed to recover')
print(s2)
print(s)
e = find_error(S[i]) # S[i] returns i-th column of S
for j in res.D[0]:
res[j, i] = e[j]
return res
## Task 8
s = "I'm trying to free your mind, Neo. But I can only show you the door. You're the one that has to walk through it."
P = bits2mat(str2bits(s)) # p[i] column is 4-bit nibble
## Ungraded task
# Use noise(A, s) to produce the transmitted message
# input: P - matrix being transmitted
print("Message w/o encoding and ecc:",
bits2str(mat2bits(P + noise(P, 0.02))).encode("utf-8"))
## Task 9
C = G * P # encode
bits_before = len(str2bits(s)) # bits before encoding
bits_after = bits_before // 4 * 7 # bits after encoding
print(bits_before, bits_after)
## Ungraded Task
CTILDE = C + noise(C, 0.02) # encoded message received
print("Message with encoding, but w/o ecc:",
bits2str(mat2bits(R * CTILDE)).encode("utf-8"))
## Task 10
def correct(A):
def decode_string_matrix(A):
return bits2str(mat2bits(A))
# Task 4.14.6 Derive original message from [1, 0, 1, 1, 0, 1, 1]
non_c = list2vec([One(), 0, One(), One(), 0, One(), One()])
syndrome = H*non_c
e = find_error(syndrome)
codeword = e + non_c
message = R * codeword
# Task 4.14.7
def find_error_matrix(s):
return coldict2mat({pos: find_error(vec) for pos, vec in mat2coldict(s).items()})
test_matrix = listlist2mat([[One(), 0], [One(), 0], [One(), One()]])
# Task 4.14.8
s = ''.join([chr(i) for i in range(256)])
assert bits2str(str2bits(s)) == s
# Task 4.14.9 & 4.14.10 encode message string to matrix of nibbles
msg = "I'm trying to free your mind, Neo."
P = bits2mat(str2bits(msg))
# Task 4.14.11 add noise to message
E = noise(P, 0.02)
EP = E + P
perturbed_msg = bits2str(mat2bits(EP))
# Task 4.14.12
C = G*P
# Task 4.14.13
CE = noise(C, 0.02)
