threshold-crc4

CRC-4 generator using polynomial x^4 + x + 1 (CRC-4-ITU).

Function

crc4(d3, d2, d1, d0) -> (crc3, crc2, crc1, crc0)

Computes 4-bit CRC for 4-bit input data.

Polynomial

G(x) = x^4 + x + 1 = 10011 (binary)

This is the ITU-T standard CRC-4 polynomial.

Parallel CRC Equations

For 4-bit input, the CRC bits are:

• crc0 = d3 XOR d0
• crc1 = d2 XOR d1 XOR d0
• crc2 = d3 XOR d1
• crc3 = d3 XOR d2

Truth Table (selected)

Data	CRC
0000	0000
0001	0011
1000	1101
1111	0010

Architecture

Each CRC bit is computed using XOR gates:

d3 d2 d1 d0
 │  │  │  │
 ├──┼──┼──┼──► XOR ──► crc0 (d3^d0)
 │  │  │  │
 │  ├──┼──┼──► XOR ──► crc3 (d3^d2)
 │  │  │  │
 ├──┼──┼──┼──► XOR ──► crc2 (d3^d1)
 │  │  │  │
 │  └──┴──┴──► XOR3 ─► crc1 (d2^d1^d0)

Parameters

Inputs	4
Outputs	4
Neurons	15
Layers	4
Parameters	61
Magnitude	50

CRC Properties

• Detects all single-bit errors
• Detects all odd numbers of bit errors
• Detects burst errors up to length 4

Usage

from safetensors.torch import load_file

w = load_file('model.safetensors')

# Append CRC to data for transmission
# Receiver recomputes CRC; if non-zero, error detected

License

MIT