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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422
use crate::noise_model::NoiseModel; use itertools::Itertools; use rand::Rng; use sparse_bin_mat::{SparseBinMat, SparseBinSlice, SparseBinVec, SparseBinVecBase}; mod edges; pub use edges::{Edge, Edges}; 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_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, bit_adjacencies: 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(parity_check_matrix: SparseBinMat) -> Self { let generator_matrix = parity_check_matrix.nullspace(); let bit_adjacencies = parity_check_matrix.transposed(); Self { generator_matrix, parity_check_matrix, bit_adjacencies, } } /// 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(generator_matrix: SparseBinMat) -> Self { let parity_check_matrix = generator_matrix.nullspace(); let bit_adjacencies = parity_check_matrix.transposed(); Self { parity_check_matrix, generator_matrix, bit_adjacencies, } } /// Returns a repetition code with the given block size. /// /// # Example /// /// ``` /// # use ldpc::{LinearCode, SparseBinMat}; /// 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 repetition_code(block_size: usize) -> Self { let generator_matrix = SparseBinMat::new(block_size, vec![(0..block_size).collect()]); Self::from_generator_matrix(generator_matrix) } /// Returns the Hamming code. /// /// # Example /// /// ``` /// # use ldpc::{LinearCode, SparseBinMat}; /// 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 hamming_code() -> Self { let parity_check_matrix = SparseBinMat::new( 7, vec![vec![3, 4, 5, 6], vec![1, 2, 5, 6], vec![0, 2, 4, 6]], ); Self::from_parity_check_matrix(parity_check_matrix) } /// Returns a builder for random LDPC codes with /// regular parity check matrix. /// /// The [`sample_with`](RandomRegularCode::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 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()) /// .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 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 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 check(&self, index: usize) -> Option<SparseBinSlice> { self.parity_check_matrix.row(index) } /// Returns the generator matrix of the code. pub fn generator_matrix(&self) -> &SparseBinMat { &self.generator_matrix } /// 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 generator(&self, index: usize) -> Option<SparseBinSlice> { self.generator_matrix.row(index) } /// Returns a matrix where the value in row i /// correspond to the check connected to bit i. pub fn bit_adjacencies(&self) -> &SparseBinMat { &self.bit_adjacencies } /// Returns the checks adjacents to the given bit or /// None if the bit is out of bound. pub fn checks_adjacent_to_bit(&self, bit: usize) -> Option<SparseBinSlice> { self.bit_adjacencies.row(bit) } /// Checks if two code define the same codespace. /// /// Two codes have the same codespace if all their 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_same_codespace_as(&other_hamming_code)); /// ``` pub fn has_same_codespace_as(&self, other: &Self) -> bool { self.block_size() == other.block_size() && (&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 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 /// /// ``` /// # use ldpc::{LinearCode, SparseBinMat, SparseBinVec, Edge}; /// 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 edges<'a>(&'a self) -> Edges<'a> { Edges::new(self) } /// Returns the product of the parity check matrix with the given message /// /// # 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 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 syndrome_of<T>(&self, message: &SparseBinVecBase<T>) -> SparseBinVec where T: std::ops::Deref<Target = [usize]>, { if message.len() != self.block_size() { panic!( "message of length {} is invalid for code with block size {}", message.len(), self.block_size() ); } &self.parity_check_matrix * message } /// Checks if a message 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), false); /// assert_eq!(hamming_code.has_codeword(&codeword), true); /// ``` /// /// # 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: std::ops::Deref<Target = [usize]>, { 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, 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); /// ``` 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) } }