brian-armstrong/fec

Source: https://github.com/brian-armstrong/fec

fec

Forward error correction for SDR, space, and satellite applications.

fec implements two error-correcting codes that show up throughout software-defined radio and spacecraft links:

• Convolutional codes with a Viterbi decoder (hard and soft decision), including the common rate-1/2 k=7, rate-1/2 k=9, rate-1/3 k=9, and rate-1/6 k=15 codes. Supports any rate from 1/2 to 1/8 and any order from k=4 to k=16. On nightly Rust, the simd feature enables a Viterbi decoder with acceleration on SSE/AVX2/AVX512.
• Reed–Solomon codes over GF(2⁸) with error and erasure decoding, including the standard CCSDS (255,223) code in both the conventional and the on-the-wire dual-basis (Berlekamp) representations.

fec started as and draws heavy inspiration from the author’s own libcorrect, a C library for forward error correction. This crate also credits Phil Karn’s libfec C library for offering an original implementation of these codes, although this crate does not borrow any source or have any relationship with that library, and the name is purely coincidental.

Standard parameters (primitive polynomials, the CCSDS dual-basis transform) are derived from the published CCSDS standard (CCSDS 131.0-B, Annex D for the dual basis).

Performance

With the simd feature, fec decodes faster than libfec on every code. Measured through libfec’s own test programs with only the codec library swapped, on a Zen4 laptop (Ryzen 7840HS). Higher is better.

Convolutional throughput is decoded payload bits per second. The Reed-Solomon rows decode a (255,223) block, first with no errors (syndromes only) and then with two symbol errors. Reed-Solomon uses no SIMD in either library, so its 32-bit and 64-bit rows differ only by pointer width.

See shim/BENCH.md for the full tables, the bit error rate comparison, the 32-bit numbers, and how to reproduce them.

Quick start

Convolutional (Viterbi)

use fec::{ConvEncoder, ConvDecoder};

// Rate-1/2, order-7 NASA code.
let polys = [0o161, 0o127];
let mut enc = ConvEncoder::new(2, 7, &polys);
let mut dec = ConvDecoder::new(2, 7, &polys);

let msg = b"hello, error correction";
let mut encoded = vec![0u8; enc.encode_len(msg.len())];
let num_bits = enc.encode(msg, &mut encoded).unwrap();

// ... encoded is corrupted in transit ...

let mut recovered = vec![0u8; msg.len()];
dec.decode_hard(&encoded, num_bits, &mut recovered).unwrap();

decode_soft takes 8-bit soft symbols instead, which corrects more errors when the demodulator can report its confidence.

Reed–Solomon

use fec::{RsEncoder, RsDecoder};

// Standard CCSDS (255,223) code.
let mut enc = RsEncoder::new_ccsds();
let mut dec = RsDecoder::new_ccsds();

let msg: Vec<u8> = (0..223).collect();
let mut block = vec![0u8; 255];
enc.encode(&msg, &mut block).unwrap();

// ... block is corrupted in transit ...

let mut recovered = vec![0u8; 223];
let corrected = dec.decode(&block, &mut recovered).unwrap();
println!("corrected {corrected} symbol error(s)");

For real spacecraft telemetry (dual-basis symbols on the wire), use encode_ccsds_dual / decode_ccsds_dual.

Compatibility

The codes are bit-compatible with libfec (Phil Karn, KA9Q), so fec can decode data Karn’s library produced and vice versa. A companion shim crate, fec-shim, exposes fec under libfec’s C ABI (init_rs_char, create_viterbi27, encode_rs_ccsds, etc) as a drop-in for existing C codebases.

Roadmap

• More widths for the Reed-Solomon encoder/decoder (narrower than GF(2⁸) and as wide as GF(2¹⁶))
• Hard-decision erasures in the convolutional (Viterbi) decoder
• Punctured codes for the convolutional encoder and decoder

License

BSD-3-Clause.