---
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- error-correction
---

# threshold-hamming1511-encoder

Hamming(15,11) encoder. Adds 4 parity bits to 11 data bits for single-error correction.

## Function

encode(d1..d11) -> [p1, p2, d1, p4, d2, d3, d4, p8, d5, d6, d7, d8, d9, d10, d11]

## Bit Positions

| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
|----------|---|---|---|---|---|---|---|---|---|----|----|----|----|----|----|
| Bit | p1 | p2 | d1 | p4 | d2 | d3 | d4 | p8 | d5 | d6 | d7 | d8 | d9 | d10 | d11 |

## Parity Equations

Each parity bit covers positions where its position number (in binary) has a 1 in that bit:

- **p1** (bit 0): positions 1,3,5,7,9,11,13,15 -> XOR(d1,d2,d4,d5,d7,d9,d11)
- **p2** (bit 1): positions 2,3,6,7,10,11,14,15 -> XOR(d1,d3,d4,d6,d7,d10,d11)
- **p4** (bit 2): positions 4,5,6,7,12,13,14,15 -> XOR(d2,d3,d4,d8,d9,d10,d11)
- **p8** (bit 3): positions 8,9,10,11,12,13,14,15 -> XOR(d5,d6,d7,d8,d9,d10,d11)

## Architecture

Each parity bit requires a 7-way XOR, implemented as a tree of 2-way XORs:

```
XOR7(a,b,c,d,e,f,g) = XOR(XOR4(a,b,c,d), XOR3(e,f,g))

XOR4(a,b,c,d) = XOR(XOR(a,b), XOR(c,d))
XOR3(e,f,g) = XOR(XOR(e,f), g)
```

Each XOR2 requires 3 neurons (OR, NAND, AND).

## Parameters

| | |
|---|---|
| Inputs | 11 |
| Outputs | 15 |
| Neurons | 86 |
| Layers | 6 |
| Parameters | 591 |
| Magnitude | 272 |

## Error Correction

When decoded, the receiver computes syndrome bits by XORing received bits at parity positions. The syndrome directly indicates the bit position of any single-bit error (0 = no error).

## Comparison to Hamming(7,4)

| Code | Data | Parity | Total | Efficiency |
|------|------|--------|-------|------------|
| Hamming(7,4) | 4 | 3 | 7 | 57% |
| Hamming(15,11) | 11 | 4 | 15 | 73% |

Larger Hamming codes are more efficient but require more complex circuits.

## Usage

```python
from safetensors.torch import load_file

w = load_file('model.safetensors')
# See model.py for reference implementation
```

## License

MIT