LDPC codes with belief propagation decoding
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README.md
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# ldpc
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Low-Density Parity-Check codes with belief propagation decoding.
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`ldpc` implements the CCSDS [131.0-B-4][ccsds] AR4JA
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(Accumulate-Repeat-4-Jagged-Accumulate) family: circulant-based
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parity-check matrices, systematic encoding, and sum-product belief
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propagation decoding. Ships with the `rate_1_2` preset (k=1024
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information bits, n=2048 transmitted bits) used on near-Earth and
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deep-space links.
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[ccsds]: https://public.ccsds.org/Pubs/131x0b4.pdf
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## Installation
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Install with opam:
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<!-- $MDX skip -->
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```sh
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$ opam install ldpc
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```
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If opam cannot find the package, it may not yet be released in the
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public `opam-repository`. Add the overlay repository, then install
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it:
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<!-- $MDX skip -->
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```sh
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$ opam repo add samoht https://tangled.org/gazagnaire.org/opam-overlay.git
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$ opam update
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$ opam install ldpc
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```
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## Usage
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The rate-1/2 code takes `k/8 = 128` data bytes and emits `n/8 = 256`
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codeword bytes:
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```ocaml
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# let data = Bytes.make 128 '\x5a' in
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let codeword = Ldpc.encode Ldpc.ccsds_rate_1_2 data in
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Bytes.length codeword
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- : int = 256
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```
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Belief-propagation decoding recovers the data from a corrupted
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codeword. `max_iter` caps the number of sum-product iterations
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(default 50):
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```ocaml
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# let data = Bytes.make 128 '\x5a' in
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let codeword = Ldpc.encode Ldpc.ccsds_rate_1_2 data in
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(* Flip a handful of bits. *)
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for i = 0 to 7 do
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Bytes.set_uint8 codeword (i * 17)
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(Bytes.get_uint8 codeword (i * 17) lxor 0x80)
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done;
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match Ldpc.decode ~max_iter:50 Ldpc.ccsds_rate_1_2 codeword with
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| Ok recovered -> Bytes.equal recovered data
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| Error _ -> false
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- : bool = true
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```
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## Licence
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ISC
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