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use crate::noise_model::NoiseModel; use crate::{SparseBinMat, SparseBinSlice, SparseBinVec}; use itertools::Itertools; use rand::Rng; mod random; pub use self::random::RandomRegularCode; /// 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. /// /// ``` /// # use ldpc::{LinearCode, SparseBinMat}; /// 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_the_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`](LinearCode::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. #[derive(Debug, PartialEq, Eq, Clone, Hash)] pub struct LinearCode { parity_check_matrix: SparseBinMat, generator_matrix: SparseBinMat, } impl LinearCode { /// Creates a new linear code from the given parity check matrix. /// /// # Example /// /// ``` /// # use ldpc::{LinearCode, SparseBinMat}; /// // 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_parity_check_matrix(matrix: SparseBinMat) -> Self { Self { generator_matrix: matrix.nullspace(), parity_check_matrix: matrix, } } /// Creates a new linear code from the given generator matrix. /// /// # Example /// /// ``` /// # use ldpc::{LinearCode, SparseBinMat}; /// // 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 from_generator_matrix(matrix: SparseBinMat) -> Self { Self { parity_check_matrix: matrix.nullspace(), generator_matrix: matrix, } } /// Returns a builder for random LDPC codes with /// regular parity check matrix. /// /// # Example /// /// ``` /// # use ldpc::LinearCode; /// 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()); /// /// 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 random_regular_code() -> RandomRegularCode { RandomRegularCode::default() } /// Returns the parity check matrix of the code. pub fn parity_check_matrix(&self) -> &SparseBinMat { &self.parity_check_matrix } /// Returns the generator matrix of the code. pub fn generator_matrix(&self) -> &SparseBinMat { &self.generator_matrix } /// Checks if two code define the same codespace. /// /// Two codes have the same codespace if all there codewords are the same. /// /// # Example /// /// ``` /// # use ldpc::{LinearCode, SparseBinMat}; /// // 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_the_same_codespace_as(&other_hamming_code)); /// ``` pub fn has_the_same_codespace_as(&self, other: &Self) -> bool { (&self.parity_check_matrix * &other.generator_matrix.transposed()).is_zero() } /// Returns the number of bits in the code. pub fn block_size(&self) -> usize { self.parity_check_matrix.number_of_columns() } /// Returns the number of rows of the parity check matrix /// of the code. pub fn number_of_checks(&self) -> usize { self.parity_check_matrix.number_of_rows() } /// Returns the number of rows of the generator matrix /// of the code. pub fn number_of_generators(&self) -> usize { self.generator_matrix.number_of_rows() } /// Returns the number of linearly independent codewords. /// /// # Example /// /// ``` /// # use ldpc::{LinearCode, SparseBinMat}; /// 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 dimension(&self) -> usize { self.generator_matrix.rank() } /// 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 minimal_distance(&self) -> Option<usize> { (1..=self.number_of_generators()) .flat_map(|n| self.generator_matrix.rows().combinations(n)) .filter_map(|generators| { let weight = generators .into_iter() .fold(SparseBinVec::zeros(self.block_size()), |sum, generator| { &sum + &generator }) .weight(); if weight > 0 { Some(weight) } else { None } }) .min() } /// Returns the product of the parity check matrix with the given error. /// /// # Example /// /// ``` /// # use ldpc::{LinearCode, SparseBinMat, SparseBinVec}; /// 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 syndrome = SparseBinVec::new(3, vec![0, 1]); /// /// assert_eq!(hamming_code.syndrome_of(&error.as_view()), syndrome); /// ``` pub fn syndrome_of(&self, error: &SparseBinSlice) -> SparseBinVec { if error.len() != self.block_size() { panic!( "error of length {} is invalid for code of size {}", error.len(), self.block_size() ); } self.parity_check_matrix.dot_with(error) } /// Checks if an operator has zero syndrome. /// /// # Example /// /// ``` /// # use ldpc::{LinearCode, SparseBinMat, SparseBinVec}; /// 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.as_view()), false); /// assert_eq!(hamming_code.has_codeword(&codeword.as_view()), true); /// ``` pub fn has_codeword(&self, operator: &SparseBinSlice) -> bool { self.syndrome_of(operator).is_zero() } /// Generates a random error with the given noise model. /// /// # Example /// /// ``` /// # use ldpc::{SparseBinMat, LinearCode}; /// use ldpc::noise_model::BinarySymmetricChannel; /// 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(0.25); /// let error = code.random_error(&noise, &mut thread_rng()); /// /// assert_eq!(error.len(), 7); /// ``` pub fn random_error<N, R>(&self, noise_model: &N, rng: &mut R) -> SparseBinVec where N: NoiseModel<Error = SparseBinVec>, R: Rng, { noise_model.sample_error_of_length(self.block_size(), rng) } }