Reed-Solomon error correction over GF(2^8)
Fix dune build: sexpt vcase_tag, tcf type annotation
- sexpt: use vcase_tag helper instead of c.tag on GADT value
- tcf: add type annotation to fix cuc_vector/cds_vector field
resolution ambiguity
+194
+24
test/interop/dune
+24
test/interop/dune
···
1
+
(test
2
+
(name test)
3
+
(libraries reed_solomon alcotest)
4
+
(deps
5
+
(source_tree traces)
6
+
(source_tree scripts)))
7
+
8
+
(rule
9
+
(alias regen-traces)
10
+
(enabled_if
11
+
(= %{env:REGEN_TRACES=0} 1))
12
+
(deps
13
+
(source_tree scripts))
14
+
(action
15
+
(with-stdout-to
16
+
rs_vectors.hex
17
+
(run python3 scripts/generate_rs.py))))
18
+
19
+
(rule
20
+
(alias regen-traces)
21
+
(enabled_if
22
+
(= %{env:REGEN_TRACES=0} 1))
23
+
(action
24
+
(diff traces/rs_vectors.hex rs_vectors.hex)))
+21
test/interop/regenerate.sh
+21
test/interop/regenerate.sh
···
1
+
#!/bin/bash
2
+
# Regenerate Reed-Solomon interop test traces.
3
+
#
4
+
# Requires: pip install reedsolo
5
+
# Usage: ./regenerate.sh
6
+
#
7
+
# Preferred method: REGEN_TRACES=1 dune build @regen-traces
8
+
# Then: dune promote
9
+
10
+
set -euo pipefail
11
+
12
+
SCRIPT_DIR="$(cd "$(dirname "$0")/scripts" && pwd)"
13
+
TRACE_DIR="$(cd "$(dirname "$0")/traces" && pwd)"
14
+
15
+
echo "Scripts: $SCRIPT_DIR"
16
+
echo "Traces: $TRACE_DIR"
17
+
echo
18
+
19
+
python3 "$SCRIPT_DIR/generate_rs.py" > "$TRACE_DIR/rs_vectors.hex"
20
+
echo "Regenerated $TRACE_DIR/rs_vectors.hex"
21
+
echo "Review with: git diff $TRACE_DIR"
+44
test/interop/scripts/generate_rs.py
+44
test/interop/scripts/generate_rs.py
···
1
+
#!/usr/bin/env python3
2
+
"""Generate Reed-Solomon test vectors using Python reedsolo.
3
+
4
+
Outputs pipe-delimited lines:
5
+
name|data_hex|codeword_hex
6
+
7
+
Uses CCSDS RS(255,223) parameters:
8
+
- Field polynomial: 0x187 (x^8 + x^7 + x^2 + x + 1)
9
+
- Primitive element (alpha): 11
10
+
- First consecutive root: 112
11
+
- t = 16 (corrects up to 16 symbol errors)
12
+
13
+
NOTE: reedsolo defaults to alpha=2 and fcr=0. The CCSDS standard uses
14
+
alpha=11, primitive poly 0x187, and fcr=112. We configure reedsolo with
15
+
these parameters explicitly.
16
+
17
+
Requires: pip install reedsolo
18
+
"""
19
+
20
+
try:
21
+
from reedsolo import RSCodec, init_tables
22
+
except ImportError:
23
+
print("ERROR: reedsolo not installed. Run: pip install reedsolo", flush=True)
24
+
raise SystemExit(1)
25
+
26
+
# CCSDS RS(255,223) parameters
27
+
NSYM = 32 # 2*t = 2*16 = 32 parity symbols
28
+
PRIM = 0x187 # primitive polynomial
29
+
ALPHA = 11 # primitive element
30
+
FCR = 112 # first consecutive root
31
+
32
+
# Initialize with CCSDS field parameters
33
+
rs = RSCodec(NSYM, prim=PRIM, generator=ALPHA, fcr=FCR)
34
+
35
+
messages = [
36
+
("zeros", bytes(223)),
37
+
("ones", bytes([0x01] * 223)),
38
+
("ascending", bytes([i % 256 for i in range(223)])),
39
+
("hello", b"Hello, Reed-Solomon!" + bytes(203)),
40
+
]
41
+
42
+
for name, data in messages:
43
+
codeword = rs.encode(data)
44
+
print(f"{name}|{data.hex()}|{bytes(codeword).hex()}")
+101
test/interop/test.ml
+101
test/interop/test.ml
···
1
+
(** Python reedsolo interop tests for ocaml-reed-solomon.
2
+
3
+
Reads committed traces from [traces/rs_vectors.hex] and verifies that the
4
+
OCaml RS(255,223) encoder produces identical codewords.
5
+
6
+
Traces generated by: [REGEN_TRACES=1 dune build @regen-traces] Oracle:
7
+
Python reedsolo (configured with CCSDS parameters) *)
8
+
9
+
let trace path = Filename.concat "traces" path
10
+
11
+
let read_file path =
12
+
let ic = open_in path in
13
+
let n = in_channel_length ic in
14
+
let s = Bytes.create n in
15
+
really_input ic s 0 n;
16
+
close_in ic;
17
+
Bytes.to_string s
18
+
19
+
let bytes_of_hex hex =
20
+
let len = String.length hex / 2 in
21
+
Bytes.init len (fun i ->
22
+
Char.chr (int_of_string ("0x" ^ String.sub hex (i * 2) 2)))
23
+
24
+
let hex_of_bytes b =
25
+
let buf = Buffer.create (Bytes.length b * 2) in
26
+
Bytes.iter
27
+
(fun c -> Buffer.add_string buf (Printf.sprintf "%02x" (Char.code c)))
28
+
b;
29
+
Buffer.contents buf
30
+
31
+
type vector = { name : string; data : bytes; expected_codeword : bytes }
32
+
33
+
let parse_vectors path =
34
+
let content = read_file path in
35
+
let lines = String.split_on_char '\n' content in
36
+
List.filter_map
37
+
(fun line ->
38
+
let line = String.trim line in
39
+
if line = "" then None
40
+
else
41
+
match String.split_on_char '|' line with
42
+
| [ name; data_hex; codeword_hex ] ->
43
+
Some
44
+
{
45
+
name;
46
+
data = bytes_of_hex data_hex;
47
+
expected_codeword = bytes_of_hex codeword_hex;
48
+
}
49
+
| _ -> Alcotest.failf "bad vector line: %s" line)
50
+
lines
51
+
52
+
let test_encode vec () =
53
+
let cfg = Reed_solomon.ccsds in
54
+
let got = Reed_solomon.encode_systematic cfg vec.data in
55
+
if got <> vec.expected_codeword then
56
+
Alcotest.failf "%s: codeword mismatch\n expected: %s\n got: %s"
57
+
vec.name
58
+
(hex_of_bytes vec.expected_codeword)
59
+
(hex_of_bytes got)
60
+
61
+
let test_roundtrip vec () =
62
+
let cfg = Reed_solomon.ccsds in
63
+
let codeword = Reed_solomon.encode_systematic cfg vec.data in
64
+
match Reed_solomon.decode cfg codeword with
65
+
| Ok decoded ->
66
+
if decoded <> vec.data then
67
+
Alcotest.failf "%s: decode mismatch after clean roundtrip" vec.name
68
+
| Error _ -> Alcotest.failf "%s: decode failed on clean codeword" vec.name
69
+
70
+
let test_error_correction vec () =
71
+
let cfg = Reed_solomon.ccsds in
72
+
let codeword = Bytes.copy vec.expected_codeword in
73
+
(* Inject 8 symbol errors (well within t=16 correction capability) *)
74
+
for i = 0 to 7 do
75
+
let pos = i * 30 in
76
+
let orig = Bytes.get codeword pos in
77
+
Bytes.set codeword pos (Char.chr (Char.code orig lxor 0xFF))
78
+
done;
79
+
match Reed_solomon.decode cfg codeword with
80
+
| Ok decoded ->
81
+
if decoded <> vec.data then
82
+
Alcotest.failf "%s: decode mismatch after error correction" vec.name
83
+
| Error _ -> Alcotest.failf "%s: decode failed with 8 errors (t=16)" vec.name
84
+
85
+
let () =
86
+
let vectors = parse_vectors (trace "rs_vectors.hex") in
87
+
Alcotest.run "rs-interop"
88
+
[
89
+
( "encode",
90
+
List.map
91
+
(fun v -> Alcotest.test_case v.name `Quick (test_encode v))
92
+
vectors );
93
+
( "roundtrip",
94
+
List.map
95
+
(fun v -> Alcotest.test_case v.name `Quick (test_roundtrip v))
96
+
vectors );
97
+
( "error-correction",
98
+
List.map
99
+
(fun v -> Alcotest.test_case v.name `Quick (test_error_correction v))
100
+
vectors );
101
+
]
+4
test/interop/traces/rs_vectors.hex
+4
test/interop/traces/rs_vectors.hex
···
1
+
zeros|00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000|000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
2
+
ones|01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101|010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
3
+
ascending|000102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f303132333435363738393a3b3c3d3e3f404142434445464748494a4b4c4d4e4f505152535455565758595a5b5c5d5e5f606162636465666768696a6b6c6d6e6f707172737475767778797a7b7c7d7e7f808182838485868788898a8b8c8d8e8f909192939495969798999a9b9c9d9e9fa0a1a2a3a4a5a6a7a8a9aaabacadaeafb0b1b2b3b4b5b6b7b8b9babbbcbdbebfc0c1c2c3c4c5c6c7c8c9cacbcccdcecfd0d1d2d3d4d5d6d7d8d9dadbdcddde|000102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f303132333435363738393a3b3c3d3e3f404142434445464748494a4b4c4d4e4f505152535455565758595a5b5c5d5e5f606162636465666768696a6b6c6d6e6f707172737475767778797a7b7c7d7e7f808182838485868788898a8b8c8d8e8f909192939495969798999a9b9c9d9e9fa0a1a2a3a4a5a6a7a8a9aaabacadaeafb0b1b2b3b4b5b6b7b8b9babbbcbdbebfc0c1c2c3c4c5c6c7c8c9cacbcccdcecfd0d1d2d3d4d5d6d7d8d9dadbdcddde1634409f25d4df227b645413120dd393f2977059c0aff86a1aa2d479bce372ee
4
+
hello|48656c6c6f2c20526565642d536f6c6f6d6f6e210000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000|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