Struct ldpc::LinearCode

pub struct LinearCode { /* fields omitted */ }

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

pub fn from_parity_check_matrix(parity_check_matrix: SparseBinMat) -> Self

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

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

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

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

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

Returns the parity check matrix of the code.

pub fn check(&self, index: usize) -> Option<SparseBinSlice<'_>>

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

Returns the generator matrix of the code.

pub fn generator(&self, index: usize) -> Option<SparseBinSlice<'_>>

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

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<'_>>

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

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

Returns the number of bits in the code.

pub fn number_of_checks(&self) -> usize

Returns the number of rows of the parity check matrix of the code.

pub fn number_of_generators(&self) -> usize

Returns the number of rows of the generator matrix of the code.

pub fn dimension(&self) -> usize

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>

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>

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]>, 

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]>, 

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, 

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

fn clone(&self) -> LinearCode

Returns a copy of the value.

pub fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for LinearCode

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Eq for LinearCode

impl Hash for LinearCode

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

pub fn hash_slice<H>(data: &[Self], state: &mut H) where
    H: Hasher, 

Feeds a slice of this type into the given Hasher.

impl PartialEq<LinearCode> for LinearCode

fn eq(&self, other: &LinearCode) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &LinearCode) -> bool

This method tests for !=.

impl StructuralEq for LinearCode

impl StructuralPartialEq for LinearCode