# ldpc

Low-Density Parity-Check codes with belief propagation decoding.

`ldpc` implements the CCSDS [131.0-B-4][ccsds] AR4JA
(Accumulate-Repeat-4-Jagged-Accumulate) family: circulant-based
parity-check matrices, systematic encoding, and sum-product belief
propagation decoding. Ships with the `rate_1_2` preset (k=1024
information bits, n=2048 transmitted bits) used on near-Earth and
deep-space links.

[ccsds]: https://public.ccsds.org/Pubs/131x0b4.pdf

## Installation

Install with opam:

<!-- $MDX skip -->
```sh
$ opam install ldpc
```

If opam cannot find the package, it may not yet be released in the
public `opam-repository`. Add the overlay repository, then install
it:

<!-- $MDX skip -->
```sh
$ opam repo add samoht https://tangled.org/gazagnaire.org/opam-overlay.git
$ opam update
$ opam install ldpc
```

## Usage

The rate-1/2 code takes `k/8 = 128` data bytes and emits `n/8 = 256`
codeword bytes:

```ocaml
# let data = Bytes.make 128 '\x5a' in
  let codeword = Ldpc.encode Ldpc.ccsds_rate_1_2 data in
  Bytes.length codeword
- : int = 256
```

Belief-propagation decoding recovers the data from a corrupted
codeword. `max_iter` caps the number of sum-product iterations
(default 50):

```ocaml
# let data = Bytes.make 128 '\x5a' in
  let codeword = Ldpc.encode Ldpc.ccsds_rate_1_2 data in
  (* Flip a handful of bits. *)
  for i = 0 to 7 do
    Bytes.set_uint8 codeword (i * 17)
      (Bytes.get_uint8 codeword (i * 17) lxor 0x80)
  done;
  match Ldpc.decode ~max_iter:50 Ldpc.ccsds_rate_1_2 codeword with
  | Ok recovered -> Bytes.equal recovered data
  | Error _ -> false
- : bool = true
```

## Licence

ISC