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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# Copyright 2025 Fabian P. Schmidt <kerel@mailbox.org>
#
# This file is part of gr-satellites
#
# SPDX-License-Identifier: GPL-3.0-or-later
#
"""
Implementation of the Mobitex FEC
This module implements the FEC algorithm used in the Mobitex protocol
for error detection and correction.
It is a (12,8,3) linear code, thus it can encode 8-bit data with 4-bit
FEC codes and detect/correct single-bit errors in the combined 12-bit words.
- Reliable two-bit error correction is not possible with this FEC scheme.
- Many collisions occur where a two-bit error produces the same syndrome as
a single-bit error.
References:
[1]: ttps://git.tu-berlin.de/rft/com/mobitub-2/-/blob/master/gr-tnc_nx/
[2]: MIT OpenCourseWare 6.02
Introduction to EECS II: Digital Communication Systems
Chapter 5: Coping with Bit Errors using Error Correction Codes
https://ocw.mit.edu/courses/
[3]: https://destevez.net/2016/09/some-notes-on-beesat-and-mobitex-nx/
"""
import sys
from enum import IntEnum
from typing import Tuple
# Matrix H, in 8 and 12 column variant
FEC_MATRIX_8b = [
0b11101100,
0b11010011,
0b10111010,
0b01110101,
]
FEC_MATRIX_12b = [
0b11101100_1000,
0b11010011_0100,
0b10111010_0010,
0b01110101_0001,
]
class Status(IntEnum):
NO_ERROR = 0
ERROR_CORRECTED = 1
ERROR_UNCORRECTABLE = 2
if sys.version_info >= (3, 10):
def calculate_even_parity(value: int) -> int:
return value.bit_count() & 1
else:
def calculate_even_parity(value: int) -> int:
"""Calculate even parity of a value, using XOR folding.
value must be 16-bit or smaller.
Returns:
Integer (0 or 1) representing (even or odd) parity
"""
value ^= (value >> 16)
value ^= (value >> 8)
value ^= (value >> 4)
value ^= (value >> 2)
value ^= (value >> 1)
return value & 1
def init_syndrome_table() -> dict:
"""Initialize the syndrome lookup table.
Returns:
Dict mapping syndromes to error positions
"""
table = {}
# Process each possible single-bit error position
for pos in range(12): # 12 bits total (8 data + 4 FEC)
# Create word with error at position pos
word = 1 << pos
# Calculate syndrome for this error
syndrome = 0
for i, mask in enumerate(FEC_MATRIX_12b):
masked = word & mask
parity = calculate_even_parity(masked)
syndrome |= (parity << (3 - i))
table[syndrome] = pos
return table
SYNDROME_TABLE = init_syndrome_table()
def encode(message: int) -> int:
"""
Takes 8-bit byte, returns 12-bit codeword.
"""
fec = 0
# Generate each FEC bit and place in correct position
for i, mask in enumerate(FEC_MATRIX_8b):
masked = message & mask
parity = calculate_even_parity(masked)
# Place parity bit in correct position (3-0)
fec |= (parity << (3 - i))
# Combine data byte and FEC into 12-bit codeword
codeword = (message << 4) | fec
return codeword
def decode(codeword: int):
"""
Takes 12-bit codeword, returns tuple of (message, corrected_fec, status).
output:
corrected_message (int): 1 control byte, error corrected
corrected_fec (int) : 4 parity bits, error corrected
status (Status) : (0 - NO ERROR,
1 - ERROR CORRECTED,
2 - ERROR UNCORRECTABLE)
"""
if not 0 <= codeword <= 0xFFF:
raise ValueError("Input must be a 12-bit value (0-4095)")
syndrome = 0
for i, row in enumerate(FEC_MATRIX_12b):
masked = codeword & row
parity = calculate_even_parity(masked)
# Build syndrome from right to left (like FEC bits)
syndrome |= (parity << (3 - i))
if syndrome == 0:
message = codeword >> 4
fec = codeword & 0x0F
return message, fec, Status.NO_ERROR
# Look up error position in syndrome table
try:
error_position = SYNDROME_TABLE[syndrome]
except KeyError:
message = codeword >> 4
fec = codeword & 0x0F
return message, fec, Status.ERROR_UNCORRECTABLE
# Correct the error by flipping the bit
corrected = codeword ^ (1 << error_position)
message = corrected >> 4
fec = corrected & 0x0F
return message, fec, Status.ERROR_CORRECTED
def split(word: int) -> Tuple[int, int]:
"""Split 12-bit codeword into data byte and FEC."""
return (word >> 4), (word & 0xF)
def pack_2b(byte0: int, byte1: int) -> bytes:
"""Pack two 12-bit codewords into three bytes."""
encoded_byte1 = byte0 >> 4
encoded_byte2 = ((byte0 & 0x0F) << 4) | (byte1 >> 8)
encoded_byte3 = byte1 & 0xFF
return bytes([encoded_byte1, encoded_byte2, encoded_byte3])
def unpack_2b(code: bytes) -> Tuple[int, int]:
"""From three bytes unpack two 12-bit codewords."""
codeword0 = (code[0] << 4) | (code[1] >> 4)
codeword1 = ((code[1] & 0x0F) << 8) | code[2]
return codeword0, codeword1
|
