#### Hamming Code

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```# Author: João Gustavo A. Amorim & Gabriel Kunz
# Author email: joaogustavoamorim@gmail.com and gabriel-kunz@uergs.edu.br
# Coding date:  apr 2019
# Black: True

"""
* This code implement the Hamming code:
https://en.wikipedia.org/wiki/Hamming_code - In telecommunication,
Hamming codes are a family of linear error-correcting codes. Hamming
codes can detect up to two-bit errors or correct one-bit errors
without detection of uncorrected errors. By contrast, the simple
parity code cannot correct errors, and can detect only an odd number
of bits in error. Hamming codes are perfect codes, that is, they
achieve the highest possible rate for codes with their block length
and minimum distance of three.

* the implemented code consists of:
* a function responsible for encoding the message (emitterConverter)
* return the encoded message
* a function responsible for decoding the message (receptorConverter)
* return the decoded message and a ack of data integrity

* how to use:
to be used you must declare how many parity bits (sizePari)
you want to include in the message.
it is desired (for test purposes) to select a bit to be set
as an error. This serves to check whether the code is working correctly.
Lastly, the variable of the message/word that must be desired to be
encoded (text).

* how this work:
declaration of variables (sizePari, be, text)

converts the message/word (text) to binary using the
text_to_bits function
encodes the message using the rules of hamming encoding
decodes the message using the rules of hamming encoding
print the original message, the encoded message and the
decoded message

forces an error in the coded text variable
decodes the message that was forced the error
print the original message, the encoded message, the bit changed
message and the decoded message
"""

# Imports
import numpy as np

# Functions of binary conversion--------------------------------------
def text_to_bits(text, encoding="utf-8", errors="surrogatepass"):
"""
>>> text_to_bits("msg")
'011011010111001101100111'
"""
bits = bin(int.from_bytes(text.encode(encoding, errors), "big"))[2:]
return bits.zfill(8 * ((len(bits) + 7) // 8))

def text_from_bits(bits, encoding="utf-8", errors="surrogatepass"):
"""
>>> text_from_bits('011011010111001101100111')
'msg'
"""
n = int(bits, 2)
return n.to_bytes((n.bit_length() + 7) // 8, "big").decode(encoding, errors) or "\0"

# Functions of hamming code-------------------------------------------
def emitter_converter(size_par, data):
"""
:param size_par: how many parity bits the message must have
:param data:  information bits
:return: message to be transmitted by unreliable medium
- bits of information merged with parity bits

>>> emitter_converter(4, "101010111111")
['1', '1', '1', '1', '0', '1', '0', '0', '1', '0', '1', '1', '1', '1', '1', '1']
"""
if size_par + len(data) <= 2**size_par - (len(data) - 1):
raise ValueError("size of parity don't match with size of data")

data_out = []
parity = []
bin_pos = [bin(x)[2:] for x in range(1, size_par + len(data) + 1)]

# sorted information data for the size of the output data
data_ord = []
# data position template + parity
data_out_gab = []
# parity bit counter
qtd_bp = 0
# counter position of data bits
cont_data = 0

for x in range(1, size_par + len(data) + 1):
# Performs a template of bit positions - who should be given,
# and who should be parity
if qtd_bp < size_par:
if (np.log(x) / np.log(2)).is_integer():
data_out_gab.append("P")
qtd_bp = qtd_bp + 1
else:
data_out_gab.append("D")
else:
data_out_gab.append("D")

# Sorts the data to the new output size
if data_out_gab[-1] == "D":
data_ord.append(data[cont_data])
cont_data += 1
else:
data_ord.append(None)

# Calculates parity
qtd_bp = 0  # parity bit counter
for bp in range(1, size_par + 1):
# Bit counter one for a given parity
cont_bo = 0
# counter to control the loop reading
cont_loop = 0
for x in data_ord:
if x is not None:
try:
aux = (bin_pos[cont_loop])[-1 * (bp)]
except IndexError:
aux = "0"
if aux == "1":
if x == "1":
cont_bo += 1
cont_loop += 1
parity.append(cont_bo % 2)

qtd_bp += 1

# Mount the message
cont_bp = 0  # parity bit counter
for x in range(0, size_par + len(data)):
if data_ord[x] is None:
data_out.append(str(parity[cont_bp]))
cont_bp += 1
else:
data_out.append(data_ord[x])

return data_out

def receptor_converter(size_par, data):
"""
>>> receptor_converter(4, "1111010010111111")
(['1', '0', '1', '0', '1', '0', '1', '1', '1', '1', '1', '1'], True)
"""
# data position template + parity
data_out_gab = []
# Parity bit counter
qtd_bp = 0
# Counter p data bit reading
cont_data = 0
data_output = []

for x in range(1, len(data) + 1):
# Performs a template of bit positions - who should be given,
#  and who should be parity
if qtd_bp < size_par and (np.log(x) / np.log(2)).is_integer():
data_out_gab.append("P")
qtd_bp = qtd_bp + 1
else:
data_out_gab.append("D")

# Sorts the data to the new output size
if data_out_gab[-1] == "D":
data_output.append(data[cont_data])
else:
cont_data += 1

# -----------calculates the parity with the data
data_out = []
parity = []
bin_pos = [bin(x)[2:] for x in range(1, size_par + len(data_output) + 1)]

#  sorted information data for the size of the output data
data_ord = []
# Data position feedback + parity
data_out_gab = []
# Parity bit counter
qtd_bp = 0
# Counter p data bit reading
cont_data = 0

for x in range(1, size_par + len(data_output) + 1):
# Performs a template position of bits - who should be given,
# and who should be parity
if qtd_bp < size_par and (np.log(x) / np.log(2)).is_integer():
data_out_gab.append("P")
qtd_bp = qtd_bp + 1
else:
data_out_gab.append("D")

# Sorts the data to the new output size
if data_out_gab[-1] == "D":
data_ord.append(data_output[cont_data])
cont_data += 1
else:
data_ord.append(None)

# Calculates parity
qtd_bp = 0  # parity bit counter
for bp in range(1, size_par + 1):
# Bit counter one for a certain parity
cont_bo = 0
# Counter to control loop reading
cont_loop = 0
for x in data_ord:
if x is not None:
try:
aux = (bin_pos[cont_loop])[-1 * (bp)]
except IndexError:
aux = "0"
if aux == "1" and x == "1":
cont_bo += 1
cont_loop += 1
parity.append(str(cont_bo % 2))

qtd_bp += 1

# Mount the message
cont_bp = 0  # Parity bit counter
for x in range(0, size_par + len(data_output)):
if data_ord[x] is None:
data_out.append(str(parity[cont_bp]))
cont_bp += 1
else:
data_out.append(data_ord[x])

return data_output, ack

# ---------------------------------------------------------------------
"""
# Example how to use

# number of parity bits
sizePari = 4

# location of the bit that will be forced an error
be = 2

# Message/word to be encoded and decoded with hamming
# text = input("Enter the word to be read: ")
text = "Message01"

# Convert the message to binary
binaryText = text_to_bits(text)

# Prints the binary of the string
print("Text input in binary is '" + binaryText + "'")

# total transmitted bits
totalBits = len(binaryText) + sizePari
print("Size of data is " + str(totalBits))

print("\n --Message exchange--")
print("Data to send ------------> " + binaryText)
dataOut = emitterConverter(sizePari, binaryText)
print("Data converted ----------> " + "".join(dataOut))
dataReceiv, ack = receptorConverter(sizePari, dataOut)
print(
+ "".join(dataReceiv)
+ "\t\t -- Data integrity: "
+ str(ack)
)

print("\n --Force error--")
print("Data to send ------------> " + binaryText)
dataOut = emitterConverter(sizePari, binaryText)
print("Data converted ----------> " + "".join(dataOut))

# forces error
dataOut[-be] = "1" * (dataOut[-be] == "0") + "0" * (dataOut[-be] == "1")
print("Data after transmission -> " + "".join(dataOut))
dataReceiv, ack = receptorConverter(sizePari, dataOut)
print(