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import numpy as np
def hdr_crc(m_header):
c4 = (m_header[0] & 0b1000) >> 3 ^ (m_header[0] & 0b0100) >> 2 ^ (m_header[0] & 0b0010) >> 1 ^ (m_header[0] & 0b0001)
c3 = (m_header[0] & 0b1000) >> 3 ^ (m_header[1] & 0b1000) >> 3 ^ (m_header[1] & 0b0100) >> 2 ^ (m_header[1] & 0b0010) >> 1 ^ (m_header[2] & 0b0001)
c2 = (m_header[0] & 0b0100) >> 2 ^ (m_header[1] & 0b1000) >> 3 ^ (m_header[1] & 0b0001) ^ (m_header[2] & 0b1000) >> 3 ^ (m_header[2] & 0b0010) >> 1
c1 = (m_header[0] & 0b0010) >> 1 ^ (m_header[1] & 0b0100) >> 2 ^ (m_header[1] & 0b0001) ^ (m_header[2] & 0b0100) >> 2 ^ (m_header[2] & 0b0010) >> 1 ^ (m_header[2] & 0b0001)
c0 = (m_header[0] & 0b0001) ^ (m_header[1] & 0b0010) >> 1 ^ (m_header[2] & 0b1000) >> 3 ^ (m_header[2] & 0b0100) >> 2 ^ (m_header[2] & 0b0010) >> 1 ^ (m_header[2] & 0b0001)
m_header3 = c4
m_header4 = c3 << 3 | c2 << 2 | c1 << 1 | c0
return m_header3, m_header4
def calculate_hdr(payload_len, CR, CRC_EN):
header_len_nibbles = 5
header = np.zeros((5), dtype =np.int16)
header[0] = (payload_len & 0xF0) >>4
header[1] = payload_len & 0x0F
header[2] = ((CR & 0x07) << 1) | (CRC_EN & 0x01)
header_to_crc_calc = (header[2]<<8) | (header[1]<<4) | (header[0])
header[3], header[4] = hdr_crc(header[0:3])
return header
#####################################################################################
def crc16(val, new_byte):
for i in range(8):
if (((val & 0x8000) >> 8) ^ (new_byte & 0x80)):
val = (val << 1) ^ 0x1021
else:
val = (val << 1)
new_byte = new_byte << 1
return val & 0xFFFF
def compute_crc(payload):
n_bytes = len(payload)
crc = 0x0000
#calculate CRC on the N-2 firsts data bytes using Poly=1021 Init=0000
for i in range( n_bytes-2):
crc = crc16(crc, payload[i])
#XOR the obtained CRC with the last 2 data bytes
crc = crc ^ payload[n_bytes-1] ^ (payload[n_bytes-2]<<8)
data_crc = np.zeros((4), dtype =np.int8)
data_crc[0] = crc & 0x000F
data_crc[1] = (crc & 0x00F0) >>4
data_crc[2] = (crc & 0x0F00) >>8
data_crc[3] = (crc & 0xF000) >>12
return data_crc
#####################################################################################
def gray_map(data, SF):
syms = np.copy(data)
for i in range(len(syms)):
syms[i] = (syms[i] - 1) % (1 << SF) # Perform modulo operation
syms[i] = syms[i] ^ (syms[i] >> 1) # Convert to Gray code
return syms
def gray_demap(data, SF):
syms = np.copy(data)
for i in range(len(data)):
s = syms[i]
for j in range(1, SF):
s = s ^ (syms[i] >> j) # Iteratively XOR with shifted versions
syms[i] = (s + 1) % (1 << SF) # Restore binary and modulo operation
return syms
#####################################################################################
def xor_integer_bits(n, num_bits):
result = 0
for i in range(num_bits):
# Extract the i-th bit using bitwise AND and right-shift operations
bit = (n >> i) & 1
# XOR the bit with the result
result ^= bit
return result
def interleave(codewords, SF, CR, LDRO):
if LDRO:
sf = SF - 2
else:
sf = SF
ppm = 4 + CR
syms = np.zeros((ppm), dtype =np.int16)
for i in range(ppm):
for j in range(sf):
bit = (codewords[(i - j - 1) % sf] >> (ppm - 1 - i)) & 1 # Extract the specific bit
syms[i] |= (bit << (sf - j - 1 )) # Set the corresponding bit in syms
if LDRO :
par = xor_integer_bits(syms[i], sf)
syms[i] = (syms[i] << 2 ) | (par<<1)
return syms
def deinterleave(syms, SF, CR, LDRO):
if LDRO:
sf = SF - 2
ldro_offset = 2
else:
sf = SF
ldro_offset = 0
ppm = 4 + CR
codewords = np.zeros((sf), dtype =np.int16)
for i in range(ppm):
for j in range(sf):
bit = (syms[i] >> (sf - j - 1 + ldro_offset)) & 1
codewords[(i-j-1)% sf] |= (bit << (ppm - 1 - i))
return codewords
#####################################################################################
whitening_seq = [
0xFF, 0xFE, 0xFC, 0xF8, 0xF0, 0xE1, 0xC2, 0x85, 0x0B, 0x17, 0x2F, 0x5E, 0xBC, 0x78, 0xF1, 0xE3,
0xC6, 0x8D, 0x1A, 0x34, 0x68, 0xD0, 0xA0, 0x40, 0x80, 0x01, 0x02, 0x04, 0x08, 0x11, 0x23, 0x47,
0x8E, 0x1C, 0x38, 0x71, 0xE2, 0xC4, 0x89, 0x12, 0x25, 0x4B, 0x97, 0x2E, 0x5C, 0xB8, 0x70, 0xE0,
0xC0, 0x81, 0x03, 0x06, 0x0C, 0x19, 0x32, 0x64, 0xC9, 0x92, 0x24, 0x49, 0x93, 0x26, 0x4D, 0x9B,
0x37, 0x6E, 0xDC, 0xB9, 0x72, 0xE4, 0xC8, 0x90, 0x20, 0x41, 0x82, 0x05, 0x0A, 0x15, 0x2B, 0x56,
0xAD, 0x5B, 0xB6, 0x6D, 0xDA, 0xB5, 0x6B, 0xD6, 0xAC, 0x59, 0xB2, 0x65, 0xCB, 0x96, 0x2C, 0x58,
0xB0, 0x61, 0xC3, 0x87, 0x0F, 0x1F, 0x3E, 0x7D, 0xFB, 0xF6, 0xED, 0xDB, 0xB7, 0x6F, 0xDE, 0xBD,
0x7A, 0xF5, 0xEB, 0xD7, 0xAE, 0x5D, 0xBA, 0x74, 0xE8, 0xD1, 0xA2, 0x44, 0x88, 0x10, 0x21, 0x43,
0x86, 0x0D, 0x1B, 0x36, 0x6C, 0xD8, 0xB1, 0x63, 0xC7, 0x8F, 0x1E, 0x3C, 0x79, 0xF3, 0xE7, 0xCE,
0x9C, 0x39, 0x73, 0xE6, 0xCC, 0x98, 0x31, 0x62, 0xC5, 0x8B, 0x16, 0x2D, 0x5A, 0xB4, 0x69, 0xD2,
0xA4, 0x48, 0x91, 0x22, 0x45, 0x8A, 0x14, 0x29, 0x52, 0xA5, 0x4A, 0x95, 0x2A, 0x54, 0xA9, 0x53,
0xA7, 0x4E, 0x9D, 0x3B, 0x77, 0xEE, 0xDD, 0xBB, 0x76, 0xEC, 0xD9, 0xB3, 0x67, 0xCF, 0x9E, 0x3D,
0x7B, 0xF7, 0xEF, 0xDF, 0xBF, 0x7E, 0xFD, 0xFA, 0xF4, 0xE9, 0xD3, 0xA6, 0x4C, 0x99, 0x33, 0x66,
0xCD, 0x9A, 0x35, 0x6A, 0xD4, 0xA8, 0x51, 0xA3, 0x46, 0x8C, 0x18, 0x30, 0x60, 0xC1, 0x83, 0x07,
0x0E, 0x1D, 0x3A, 0x75, 0xEA, 0xD5, 0xAA, 0x55, 0xAB, 0x57, 0xAF, 0x5F, 0xBE, 0x7C, 0xF9, 0xF2,
0xE5, 0xCA, 0x94, 0x28, 0x50, 0xA1, 0x42, 0x84, 0x09, 0x13, 0x27, 0x4F, 0x9F, 0x3F, 0x7F
]
def whitening(payload):
nibbles = np.zeros((2*len(payload)), dtype =np.int8)
for i in range(len(payload)):
low_nib = (payload[i] & 0x0F) ^ (whitening_seq[i] & 0x0F)
high_nib = (payload[i] & 0xF0)>>4 ^ (whitening_seq[i] & 0xF0)>>4
nibbles[2*i] = low_nib
nibbles[2*i+1] = high_nib
return nibbles
def dewhitening(nibbles):
payload = np.zeros((len(nibbles)//2), dtype =np.int8)
for i in range(len(nibbles)//2):
low_nib = nibbles[2*i] ^ (whitening_seq[i] & 0x0F)
high_nib = nibbles[2*i+1] ^ (whitening_seq[i] & 0xF0)>>4
payload[i] = (high_nib << 4) | low_nib
return payload
def lfsr(state, taps):
feedback = 0
for tap in taps:
feedback ^= (state >> (tap - 1)) & 1 # Extract the bit and XOR it
# Shift the register and insert the feedback bit at the leftmost position
state = ((state << 1) | feedback) & 0xFF
return state
def whitening_lfsr(payload):
state = 0xFF
nibbles = np.zeros((2*len(payload)), dtype =np.int8)
for i in range(len(payload)):
low_nib = (payload[i] & 0x0F) ^ (state & 0x0F)
high_nib = (payload[i] & 0xF0)>>4 ^ (state & 0xF0)>>4
nibbles[2*i] = low_nib
nibbles[2*i+1] = high_nib
state = lfsr(state,[8, 6, 5, 4])
return nibbles
def dewhitening_lfsr(nibbles):
state = 0xFF
payload = np.zeros((len(nibbles)//2), dtype =np.uint8)
for i in range(len(nibbles)//2):
low_nib = nibbles[2*i] ^ (state & 0x0F)
high_nib = nibbles[2*i+1] ^ (state & 0xF0)>>4
payload[i] = (high_nib << 4) | low_nib
state = lfsr(state,[8, 6, 5, 4])
return payload
#####################################################################################
def hamming_encode(data, CR):
data_len = len(data)
codewords = np.zeros((len(data)), dtype =np.int8)
for i in range(data_len):
d0 = (data[i] >> 3) & 1
d1 = (data[i] >> 2) & 1
d2 = (data[i] >> 1) & 1
d3 = (data[i] >> 0) & 1
if (CR==1):
p4 = d0 ^ d1 ^ d2 ^ d3
codewords[i] = d3<<4 | d2<<3 | d1<<2 | d0<<1 | p4
else:
p0 = d3 ^ d2 ^ d1
p1 = d2 ^ d1 ^ d0
p2 = d3 ^ d2 ^ d0
p3 = d3 ^ d1 ^ d0
codewords[i] = (d3<<7 | d2<<6 | d1<<5 | d0<<4 | p0<<3 | p1<<2 | p2<<1 | p3) >> (4-CR)
return codewords
def hamming_decode(codewords, CR):
codewords_len = len(codewords)
data = np.zeros((codewords_len), dtype =np.int8)
for i in range(codewords_len):
cw = codewords[i] << (4-CR)
c0 = (cw >> 7) & 1
c1 = (cw >> 6) & 1
c2 = (cw >> 5) & 1
c3 = (cw >> 4) & 1
c4 = (cw >> 3) & 1
c5 = (cw >> 2) & 1
c6 = (cw >> 1) & 1
cp = (cw >> 0) & 1
if (CR > 2) :
s0 = c0 ^ c1 ^ c2 ^ c4
s1 = c1 ^ c2 ^ c3 ^ c5
s2 = c0 ^ c1 ^ c3 ^ c6
syndrom = s0 | (s1 << 1) | (s2 << 2)
if syndrom == 5 :
c0 = (1-c0)
elif syndrom == 7 :
c1 = (1-c1)
elif syndrom == 3 :
c2 = (1-c2)
elif syndrom == 6 :
c3 = (1-c3)
data[i] = (c3 << 3) | (c2 << 2) | (c1 << 1) | c0
return data
#####################################################################################
def payload_to_symbol(input_data, SF, CR, CRC_EN, LDRO):
whitened_data = whitening_lfsr(input_data)
header = calculate_hdr(len(input_data), CR, CRC_EN)
data_crc = compute_crc(input_data)
if CRC_EN:
pkt = np.concatenate((header,whitened_data,data_crc))
else :
pkt = np.concatenate((header,whitened_data))
ldro_hdr = 1 if SF>6 else 0
first_encoded = hamming_encode(pkt[0:SF-2*ldro_hdr],4)
rest_encoded = hamming_encode(pkt[SF-2*ldro_hdr :],CR)
n_blocks = int(np.ceil(len(rest_encoded)/(SF - 2*LDRO))); #Number of blocks in payload
padded_encoded = np.pad(rest_encoded,(0,(n_blocks*SF - len(rest_encoded))))
n_symb = 8 + n_blocks*(4+CR)
binary_symbols = np.zeros((n_symb),dtype=np.int16)
binary_symbols[0:8] = interleave(first_encoded,SF,4,ldro_hdr )
sf = SF-2*LDRO
for i in range(n_blocks):
binary_symbols[8+i*(4+CR) : 8+(i+1)*(4+CR)] = interleave(padded_encoded[i*sf : (i+1)*sf],SF,CR,LDRO )
symbols = gray_demap(binary_symbols,SF)
return symbols
#####################################################################################
def symbols_to_payload(symbols,SF,LDRO, verbose = False):
ldro_hdr = 1 if SF>6 else 0
degrayed_symbols = gray_map(symbols,SF)
if verbose:
print("Degrayed symbols :")
print("------------------------------")
print(degrayed_symbols)
print("---------------------------------")
first_block = deinterleave(degrayed_symbols[:8],SF,4,ldro_hdr)
firstBlen = len(first_block)
decoded_hdr = hamming_decode(first_block,4)
dec_hdr_len = (decoded_hdr[0]<<4)|(decoded_hdr[1])
dec_crc_en = (decoded_hdr[2] & 0x01)
dec_hdr_cr = (decoded_hdr[2] >>1) & 0x03
dec_hdr_crc =((decoded_hdr[3] & 0x01) << 4) | decoded_hdr[4]
hdrCRC3,hdrCRC4 = hdr_crc(decoded_hdr[0:3])
rec_hdr_cr = (hdrCRC3<< 4) | hdrCRC4
n_received_blocks = int((len(degrayed_symbols)-8)/(4+dec_hdr_cr))
other_blocks = np.zeros((n_received_blocks*(SF- 2*LDRO)),dtype=np.int16)
sf = SF - 2*LDRO
for i in range(n_received_blocks):
other_blocks[i*sf : (i+1)*sf] = deinterleave(degrayed_symbols[8+i*(4+dec_hdr_cr) : 8+(i+1)*(4+dec_hdr_cr)],SF,dec_hdr_cr,LDRO )
if verbose:
print("Deinterleaved symbols")
print("----------1st block ----------")
print(first_block)
print("----------2nd block ----------")
print(other_blocks)
print("------------------------------")
decoded_pay = np.concatenate((decoded_hdr[5:],hamming_decode(other_blocks,dec_hdr_cr)))
if verbose:
print("Decoded payload")
print("------------------------------")
print(decoded_pay)
print("------------------------------")
dewhitened_payload = dewhitening_lfsr(decoded_pay)
if verbose:
print("Dewhitened payload")
print("------------------------------")
print(dewhitened_payload)
print("------------------------------")
print("Payload len : %d "%(dec_hdr_len))
print("Code rate : 4/%d"%(4+dec_hdr_cr))
print("Header CRC : %d vs %d"%(dec_hdr_crc,rec_hdr_cr))
if dec_crc_en :
idx = dec_hdr_len*2
rec_data_crc = compute_crc(dewhitened_payload[:dec_hdr_len])
print("CRC is enabled : %s vs %s"%(decoded_pay[idx:idx+4],rec_data_crc))
print(''.join(chr(d) for d in dewhitened_payload[:dec_hdr_len]))
#####################################################################################