1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
use super::{Decoder, DecodingResult};
use crate::ParityCheckMatrix;
use rand::{thread_rng, Rng};
pub struct ErasureDecoder<'a> {
checks: &'a ParityCheckMatrix,
erasure_prob: f64,
}
impl<'a> ErasureDecoder<'a> {
pub fn new(checks: &'a ParityCheckMatrix, erasure_prob: f64) -> Self {
if erasure_prob < 0.0 || erasure_prob > 1.0 {
panic!("invalid probability");
}
Self {
checks,
erasure_prob,
}
}
}
impl<'a> Decoder for ErasureDecoder<'a> {
type Error = Vec<usize>;
type Result = ErasureResult;
fn decode(&self, error: &Self::Error) -> Self::Result {
let erased_parity_check = self.checks.keep(error);
if error.len() - erased_parity_check.rank() == 0 {
ErasureResult::Succeed
} else {
ErasureResult::Failed
}
}
fn random_error(&self) -> Vec<usize> {
let mut rng = thread_rng();
(0..self.checks.n_bits())
.filter(|_| rng.gen::<f64>() < self.erasure_prob)
.collect()
}
}
#[derive(Debug, PartialEq, Eq)]
pub enum ErasureResult {
Failed,
Succeed,
}
impl DecodingResult for ErasureResult {
fn succeed(&self) -> bool {
self == &Self::Succeed
}
}
#[cfg(test)]
mod test {
use super::*;
#[test]
fn repetition_code() {
let matrix = ParityCheckMatrix::new(vec![vec![0, 1], vec![1, 2]], 3);
let decoder = ErasureDecoder::new(&matrix, 0.2);
assert_eq!(decoder.decode(&vec![]), ErasureResult::Succeed);
for i in 0..=2 {
assert_eq!(decoder.decode(&vec![i]), ErasureResult::Succeed);
for j in (i + 1)..=2 {
assert_eq!(decoder.decode(&vec![i, j]), ErasureResult::Succeed);
}
}
assert_eq!(decoder.decode(&vec![0, 1, 2]), ErasureResult::Failed);
}
#[test]
fn hamming_code() {
let matrix = ParityCheckMatrix::new(
vec![vec![0, 1, 2, 4], vec![0, 1, 3, 5], vec![0, 2, 3, 6]],
7,
);
let decoder = ErasureDecoder::new(&matrix, 0.2);
assert_eq!(decoder.decode(&vec![]), ErasureResult::Succeed);
for i in 0..=6 {
assert_eq!(decoder.decode(&vec![i]), ErasureResult::Succeed);
for j in (i + 1)..=6 {
assert_eq!(decoder.decode(&vec![i, j]), ErasureResult::Succeed);
}
}
assert_eq!(decoder.decode(&vec![0, 1, 2]), ErasureResult::Succeed);
assert_eq!(decoder.decode(&vec![2, 4, 5]), ErasureResult::Succeed);
assert_eq!(decoder.decode(&vec![0, 1, 4]), ErasureResult::Succeed);
assert_eq!(decoder.decode(&vec![3, 4, 5]), ErasureResult::Succeed);
assert_eq!(decoder.decode(&vec![2, 4, 6]), ErasureResult::Failed);
assert_eq!(decoder.decode(&vec![1, 2, 3]), ErasureResult::Failed);
assert_eq!(decoder.decode(&vec![0, 3, 4]), ErasureResult::Failed);
assert_eq!(decoder.decode(&vec![0, 2, 5]), ErasureResult::Failed);
assert_eq!(
decoder.decode(&vec![0, 1, 2, 3, 4, 5, 6]),
ErasureResult::Failed
);
}
}