Struct ldpc::LinearCode [−][src]
An implementation of linear codes optimized for LDPC codes.
A code can be define from either a parity check matrix H
or a generator matrix G
.
These matrices have the property that H G^T = 0
.
Example
This is example shows 2 way to define the Hamming code.
let parity_check_matrix = SparseBinMat::new( 7, vec![vec![0, 1, 2, 4], vec![0, 1, 3, 5], vec![0, 2, 3, 6]] ); let generator_matrix = SparseBinMat::new( 7, vec![vec![0, 4, 5, 6], vec![1, 4, 5], vec![2, 4, 6], vec![3, 5, 6]] ); let code_from_parity = LinearCode::from_parity_check_matrix(parity_check_matrix); let code_from_generator = LinearCode::from_generator_matrix(generator_matrix); assert!(code_from_parity.has_same_codespace_as(&code_from_generator));
Comparison
Use the ==
if you want to know if 2 codes
have exactly the same parity check matrix and
generator matrix.
However, since there is freedom in the choice of
parity check matrix and generator matrix for the same code,
use has_the_same_codespace_as
method
if you want to know if 2 codes define the same codespace even
if they may have different parity check matrix or generator matrix.
Implementations
impl LinearCode
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pub fn from_parity_check_matrix(parity_check_matrix: SparseBinMat) -> Self
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Creates a new linear code from the given parity check matrix.
Example
// 3 bits repetition code. let matrix = SparseBinMat::new(3, vec![vec![0, 1], vec![1, 2]]); let code = LinearCode::from_parity_check_matrix(matrix); assert_eq!(code.block_size(), 3); assert_eq!(code.dimension(), 1); assert_eq!(code.minimal_distance(), Some(3));
pub fn from_generator_matrix(generator_matrix: SparseBinMat) -> Self
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Creates a new linear code from the given generator matrix.
Example
// 3 bits repetition code. let matrix = SparseBinMat::new(3, vec![vec![0, 1, 2]]); let code = LinearCode::from_generator_matrix(matrix); assert_eq!(code.block_size(), 3); assert_eq!(code.dimension(), 1); assert_eq!(code.minimal_distance(), Some(3));
pub fn repetition_code(block_size: usize) -> Self
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Returns a repetition code with the given block size.
Example
let matrix = SparseBinMat::new(3, vec![vec![0, 1], vec![1, 2]]); let code = LinearCode::from_parity_check_matrix(matrix); assert!(code.has_same_codespace_as(&LinearCode::repetition_code(3)));
pub fn hamming_code() -> Self
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Returns the Hamming code.
Example
let matrix = SparseBinMat::new( 7, vec![vec![3, 4, 5, 6], vec![1, 2, 5, 6], vec![0, 2, 4, 6]], ); let code = LinearCode::from_parity_check_matrix(matrix); assert!(code.has_same_codespace_as(&LinearCode::hamming_code()));
pub fn random_regular_code() -> RandomRegularCode
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Returns a builder for random LDPC codes with regular parity check matrix.
The sample_with
method returns
an error if the block size times the bit's degree is not equal
to the number of checks times the bit check's degree.
Example
use rand::thread_rng; let code = LinearCode::random_regular_code() .block_size(20) .number_of_checks(15) .bit_degree(3) .check_degree(4) .sample_with(&mut thread_rng()) .unwrap(); // 20 * 3 == 15 * 4 assert_eq!(code.block_size(), 20); assert_eq!(code.number_of_checks(), 15); assert_eq!(code.parity_check_matrix().number_of_ones(), 60);
pub fn parity_check_matrix(&self) -> &SparseBinMat
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Returns the parity check matrix of the code.
pub fn check(&self, index: usize) -> Option<SparseBinSlice<'_>>
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Returns the check at the given index or None if the index is out of bound.
That is, this returns the row of the parity check matrix with the given index.
pub fn generator_matrix(&self) -> &SparseBinMat
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Returns the generator matrix of the code.
pub fn generator(&self, index: usize) -> Option<SparseBinSlice<'_>>
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Returns the generator at the given index or None if the index is out of bound.
That is, this returns the row of the generator matrix with the given index.
pub fn bit_adjacencies(&self) -> &SparseBinMat
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Returns a matrix where the value in row i correspond to the check connected to bit i.
pub fn checks_adjacent_to_bit(&self, bit: usize) -> Option<SparseBinSlice<'_>>
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Returns the checks adjacents to the given bit or None if the bit is out of bound.
pub fn has_same_codespace_as(&self, other: &Self) -> bool
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Checks if two code define the same codespace.
Two codes have the same codespace if all their codewords are the same.
Example
// The Hamming code let parity_check_matrix = SparseBinMat::new( 7, vec![vec![0, 1, 2, 4], vec![0, 1, 3, 5], vec![0, 2, 3, 6]] ); let hamming_code = LinearCode::from_parity_check_matrix(parity_check_matrix); // Same but with the add the first check to the other two. let parity_check_matrix = SparseBinMat::new( 7, vec![vec![0, 1, 2, 4], vec![2, 3, 4, 5], vec![1, 3, 4, 6]] ); let other_hamming_code = LinearCode::from_parity_check_matrix(parity_check_matrix); assert!(hamming_code.has_same_codespace_as(&other_hamming_code));
pub fn block_size(&self) -> usize
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Returns the number of bits in the code.
pub fn number_of_checks(&self) -> usize
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Returns the number of rows of the parity check matrix of the code.
pub fn number_of_generators(&self) -> usize
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Returns the number of rows of the generator matrix of the code.
pub fn dimension(&self) -> usize
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Returns the number of linearly independent codewords.
Example
let parity_check_matrix = SparseBinMat::new( 7, vec![vec![0, 1, 2, 4], vec![0, 1, 3, 5], vec![0, 2, 3, 6]] ); let hamming_code = LinearCode::from_parity_check_matrix(parity_check_matrix); assert_eq!(hamming_code.dimension(), 4);
pub fn minimal_distance(&self) -> Option<usize>
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Returns the weight of the smallest non trivial codeword or None if the code have no codeword.
Warning
The execution time of this method scale exponentially with the dimension of the code.
pub fn edges<'a>(&'a self) -> Edges<'a>ⓘ
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Returns an iterator over all edges of the Tanner graph associated with the parity check matrix of the code.
That is, this returns an iterator of over the coordinates (i, j) such that H_ij = 1 with H the parity check matrix.
Example
let parity_check_matrix = SparseBinMat::new( 4, vec![vec![0, 1], vec![0, 3], vec![1, 2]] ); let code = LinearCode::from_parity_check_matrix(parity_check_matrix); let mut edges = code.edges(); assert_eq!(edges.next(), Some(Edge { bit: 0, check: 0})); assert_eq!(edges.next(), Some(Edge { bit: 1, check: 0})); assert_eq!(edges.next(), Some(Edge { bit: 0, check: 1})); assert_eq!(edges.next(), Some(Edge { bit: 3, check: 1})); assert_eq!(edges.next(), Some(Edge { bit: 1, check: 2})); assert_eq!(edges.next(), Some(Edge { bit: 2, check: 2})); assert_eq!(edges.next(), None);
pub fn syndrome_of<T>(&self, message: &SparseBinVecBase<T>) -> SparseBinVec where
T: Deref<Target = [usize]>,
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T: Deref<Target = [usize]>,
Returns the product of the parity check matrix with the given message
Example
let parity_check_matrix = SparseBinMat::new( 7, vec![vec![0, 1, 2, 4], vec![0, 1, 3, 5], vec![0, 2, 3, 6]] ); let hamming_code = LinearCode::from_parity_check_matrix(parity_check_matrix); let message = SparseBinVec::new(7, vec![0, 2, 4]); let syndrome = SparseBinVec::new(3, vec![0, 1]); assert_eq!(hamming_code.syndrome_of(&message.as_view()), syndrome);
Panic
Panics if the message have a different length then code block size.
pub fn has_codeword<T>(&self, operator: &SparseBinVecBase<T>) -> bool where
T: Deref<Target = [usize]>,
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T: Deref<Target = [usize]>,
Checks if a message has zero syndrome.
Example
let parity_check_matrix = SparseBinMat::new( 7, vec![vec![0, 1, 2, 4], vec![0, 1, 3, 5], vec![0, 2, 3, 6]] ); let hamming_code = LinearCode::from_parity_check_matrix(parity_check_matrix); let error = SparseBinVec::new(7, vec![0, 2, 4]); let codeword = SparseBinVec::new(7, vec![2, 3, 4, 5]); assert_eq!(hamming_code.has_codeword(&error), false); assert_eq!(hamming_code.has_codeword(&codeword), true);
Panic
Panics if the message have a different length then code block size.
pub fn random_error<N, R>(&self, noise_model: &N, rng: &mut R) -> SparseBinVec where
N: NoiseModel<Error = SparseBinVec>,
R: Rng,
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N: NoiseModel<Error = SparseBinVec>,
R: Rng,
Generates a random error with the given noise model.
Example
use ldpc::noise_model::{BinarySymmetricChannel, Probability}; use rand::thread_rng; let parity_check_matrix = SparseBinMat::new( 7, vec![vec![0, 1, 2, 4], vec![0, 1, 3, 5], vec![0, 2, 3, 6]] ); let code = LinearCode::from_parity_check_matrix(parity_check_matrix); let noise = BinarySymmetricChannel::with_probability(Probability::new(0.25)); let error = code.random_error(&noise, &mut thread_rng()); assert_eq!(error.len(), 7);
Trait Implementations
impl Clone for LinearCode
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fn clone(&self) -> LinearCode
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pub fn clone_from(&mut self, source: &Self)
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impl Debug for LinearCode
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impl Eq for LinearCode
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impl Hash for LinearCode
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fn hash<__H: Hasher>(&self, state: &mut __H)
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pub fn hash_slice<H>(data: &[Self], state: &mut H) where
H: Hasher,
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H: Hasher,
impl PartialEq<LinearCode> for LinearCode
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fn eq(&self, other: &LinearCode) -> bool
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fn ne(&self, other: &LinearCode) -> bool
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impl StructuralEq for LinearCode
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impl StructuralPartialEq for LinearCode
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Auto Trait Implementations
impl RefUnwindSafe for LinearCode
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impl Send for LinearCode
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impl Sync for LinearCode
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impl Unpin for LinearCode
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impl UnwindSafe for LinearCode
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Blanket Implementations
impl<T> Any for T where
T: 'static + ?Sized,
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T: 'static + ?Sized,
impl<T> Borrow<T> for T where
T: ?Sized,
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T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
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T: ?Sized,
pub fn borrow_mut(&mut self) -> &mut T
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impl<Q, K> Equivalent<K> for Q where
K: Borrow<Q> + ?Sized,
Q: Eq + ?Sized,
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K: Borrow<Q> + ?Sized,
Q: Eq + ?Sized,
pub fn equivalent(&self, key: &K) -> bool
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impl<T> From<T> for T
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impl<T, U> Into<U> for T where
U: From<T>,
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U: From<T>,
impl<T> ToOwned for T where
T: Clone,
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T: Clone,
type Owned = T
The resulting type after obtaining ownership.
pub fn to_owned(&self) -> T
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pub fn clone_into(&self, target: &mut T)
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impl<T, U> TryFrom<U> for T where
U: Into<T>,
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U: Into<T>,
type Error = Infallible
The type returned in the event of a conversion error.
pub fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>
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impl<T, U> TryInto<U> for T where
U: TryFrom<T>,
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U: TryFrom<T>,
type Error = <U as TryFrom<T>>::Error
The type returned in the event of a conversion error.
pub fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>
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impl<V, T> VZip<V> for T where
V: MultiLane<T>,
V: MultiLane<T>,