def show_example():
# Configurable parameters
field = fieldmath.BinaryField(0x11D)
generator = 0x02
msglen = 8
ecclen = 5
rs = reedsolomon.ReedSolomon(field, generator, msglen, ecclen)
# Generate random message
message = [random.randrange(field.size) for _ in range(msglen)]
print("Original message: {}".format(message))
# Encode message to produce codeword
codeword = rs.encode(message)
print("Encoded codeword: {}".format(codeword))
# Perturb some values in the codeword
probability = float(ecclen // 2) / (msglen + ecclen)
perturbed = 0
for i in range(len(codeword)):
if random.random() < probability:
codeword[i] ^= random.randrange(1, field.size)
perturbed += 1
print("Number of values perturbed: {}".format(perturbed))
print("Perturbed codeword: {}".format(codeword))
# Try to decode the codeword
decoded = rs.decode(codeword)
print("Decoded message: {}".format(decoded if (decoded is not None) else "Failure"))
print("")
def show_prime_example():
# Configurable parameters
field = fieldmath.PrimeField(97)
generator = 5
msglen = 9
ecclen = 4
rs = reedsolomon.ReedSolomon(field, generator, msglen, ecclen)
# Generate random message
message = [random.randrange(field.modulus) for _ in range(msglen)]
print(f"Original message: {message}")
# Encode message to produce codeword
codeword = rs.encode(message)
print(f"Encoded codeword: {codeword}")
# Perturb some values in the codeword
probability = (ecclen // 2) / (msglen + ecclen)
perturbed = 0
for i in range(len(codeword)):
if random.random() < probability:
codeword[i] = field.add(codeword[i],
random.randrange(1, field.modulus))
perturbed += 1
print(f"Number of values perturbed: {perturbed}")
print(f"Perturbed codeword: {codeword}")
# Try to decode the codeword
decoded = rs.decode(codeword)
print(
f"Decoded message: {decoded if (decoded is not None) else 'Failure'}")
print()
def test_correctness():
# Field parameters
field = fieldmath.BinaryField(0x11D)
generator = 0x02
# Run forever unless an exception is thrown or unexpected behavior is encountered
testduration = 10.0 # In seconds
while True:
# Choose random Reed-Solomon parameters
msglen = random.randrange(1, field.size)
ecclen = random.randrange(1, field.size)
codewordlen = msglen + ecclen
if codewordlen > field.size - 1:
continue
numerrors = random.randrange(codewordlen + 1)
rs = reedsolomon.ReedSolomon(field, generator, msglen, ecclen)
# Do as many trials as possible in a fixed amount of time
numsuccess = 0
numwrong = 0
numfailure = 0
starttime = time.time()
while time.time() - starttime < testduration:
# Generate random message
message = [random.randrange(field.size) for _ in range(msglen)]
# Encode message to codeword
codeword = rs.encode(message)
# Perturb values in the codeword
indexes = [i for i in range(codewordlen)]
for i in range(numerrors):
# Partial Durstenfeld shuffle
j = random.randrange(i, codewordlen)
indexes[i], indexes[j] = indexes[j], indexes[i]
# Actual perturbation
codeword[indexes[i]] ^= random.randrange(1, field.size)
# Try to decode the codeword, and evaluate result
decoded = rs.decode(codeword)
if decoded == message:
numsuccess += 1
elif numerrors <= ecclen // 2:
raise AssertionError("Decoding should have succeeded")
elif decoded is not None:
numwrong += 1
else:
numfailure += 1
# Print parameters and statistics for this round
print(
f"msgLen={msglen}, eccLen={ecclen}, codewordLen={codewordlen}, numErrors={numerrors}; numTrials={numsuccess + numwrong + numfailure}, numSuccess={numsuccess}, numWrong={numwrong}, numFailure={numfailure}"
)