---
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- error-detection
- crc
---

# 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

```python
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