public static MatrixInt CalculateGeneratorMatrixAlt(ILinearCode linearCode) { var generatorMatrix = new MatrixInt(linearCode.K, linearCode.N); var system = linearCode.ParityCheckMatrix.Clone(); MatrixInt solution = null; try { solution = MatrixAlgorithms.Solve(system, linearCode.GaloisField); } catch (SolveMatrixException) { throw new LinearCodeException("Could not produce correct Generator matrix from provided ParityCheck matrix."); } #region Assemble generator matrix for (int i = 0; i < linearCode.K; i++) { for (int j = 0; j < solution.RowCount; j++) { generatorMatrix[i, j] = solution[j, i]; } if (solution.RowCount < linearCode.N) { generatorMatrix[i, linearCode.N - linearCode.K + i] = 1; } } #endregion return(generatorMatrix); }
public static MatrixInt MatrixInverse(MatrixInt matrix, GaloisField galoisField) { var identity = Helper.GenerateIdentityMatrix(matrix.RowCount); var toSolve = matrix | (identity); var inverse = MatrixAlgorithms.Solve(toSolve, galoisField); return(inverse); }
public static MatrixInt CalculateGeneratorMatrix(ILinearCode linearCode) { var generatorMatrix = new MatrixInt(linearCode.K, linearCode.N); #region Init for (int i = 0; i < linearCode.K; i++) { for (int j = 0; j < linearCode.K; j++) { if (i == j) { generatorMatrix[i, j] = 1; } else { generatorMatrix[i, j] = 0; } } } #endregion #region Solve k systems of linear equasions on field elements for (int i = 0; i < linearCode.K; i++) { var systemA = linearCode.ParityCheckMatrix.GetRangeOfColumns(new RangeInt(linearCode.K, linearCode.N)); var systemB = systemA | linearCode.ParityCheckMatrix.GetColumn(i); Debug.WriteLine(systemB); MatrixInt systemSolution; try { systemSolution = MatrixAlgorithms.Solve(systemB, linearCode.GaloisField); } catch (SolveMatrixException) { throw new LinearCodeException("Could not produce correct Generator matrix from provided ParityCheck matrix."); } #region CopyResults for (int row = 0; row < systemSolution.RowCount; row++) { generatorMatrix[i, row + linearCode.K] = systemSolution[row, systemSolution.ColumnCount - 1]; } #endregion } #endregion return(generatorMatrix); }
public static int[] LocateErrors(ILinearCode linearCode, MatrixInt syndrome) { #region Error locator polynomial var rowCount = linearCode.T; var columnCount = linearCode.T + 1; var system = new int[rowCount, columnCount]; for (int row = 0; row < rowCount; row++) { for (int col = 0; col < columnCount; col++) { system[row, col] = syndrome[0, row + col]; } } var coefficients = MatrixAlgorithms.Solve(new MatrixInt(system), linearCode.GaloisField).Transpose(); #endregion #region Calculate Error Positions var errorLocators = new int[linearCode.N]; for (int position = 0, word = 1; position < linearCode.N; position++, word++) { var sum = coefficients[0, 0]; for (int i = 1; i < coefficients.ColumnCount; i++) { var wordPower = linearCode.GaloisField.Power(word, i); var wordToAdd = linearCode.GaloisField.MultiplyWords(coefficients[0, i], wordPower); sum = linearCode.GaloisField.AddWords(sum, wordToAdd); } var lastWord = linearCode.GaloisField.Power(word, linearCode.T); sum = linearCode.GaloisField.AddWords(sum, lastWord); errorLocators[position] = sum; } #endregion return(errorLocators); }
public static int[] LocateErrors(ILinearCode linearCode, MatrixInt syndrome, ParityCheckMatrixGeneratorEllyptic generator) { #region Error locator polynomial var rowCount = linearCode.T; var columnCount = linearCode.T + 1; var system = new int[rowCount, columnCount]; for (int row = 0; row < rowCount; row++) { for (int col = 0; col < columnCount - 1; col++) { system[row, col] = syndrome[0, generator.Terms[(row + col), linearCode.T - 2]]; } system[row, columnCount - 1] = syndrome[0, generator.Terms[row, linearCode.T - 1]]; } var coefficients = MatrixAlgorithms.Solve(new MatrixInt(system), linearCode.GaloisField).Transpose(); #endregion #region Calculate Error Positions var errorLocators = new int[linearCode.N]; for (int position = 0; position < linearCode.N; position++) { var sum = 0; for (int i = 0; i < linearCode.T; i++) { var wordToAdd = linearCode.GaloisField.MultiplyWords(coefficients[0, i], linearCode.GaloisField.Power(generator.Points[position].x, i)); sum = linearCode.GaloisField.AddWords(sum, wordToAdd); } sum = linearCode.GaloisField.AddWords(sum, generator.Points[position].y); errorLocators[position] = sum; } #endregion return(errorLocators); }
public static MatrixInt DecodeAndCorrect(ILinearCode linearCode, MatrixInt message, ParityCheckMatrixGeneratorEllyptic generator) { if (message.ColumnCount != linearCode.ParityCheckMatrix.ColumnCount) { throw new DimensionMismatchException("Incorrect length of message. Meesage length should be equal number of columns in parity check matrix."); } #region Calculate syndrome var syndrome = MatrixAlgorithms.DotMultiplication(message, linearCode.ParityCheckMatrix.Transpose(), linearCode.GaloisField); #endregion #region Locate errors var errorLocators = ErrorLocatorEllyptic.LocateErrors(linearCode, syndrome, generator); var errorCount = errorLocators.Where(v => v == 0).Count(); #endregion Debug.WriteLine(linearCode.ParityCheckMatrix); #region Caclulate Error vector var system = new MatrixInt(linearCode.D, errorCount); for (int row = 0; row < linearCode.D; row++) { for (int col = 0, i = 0; col < linearCode.N; col++) { if (errorLocators[col] == 0) { system[row, i] = linearCode.ParityCheckMatrix[row, col]; i++; } } } Debug.WriteLine(system); system |= syndrome.Transpose(); Debug.WriteLine(system); var errorVectorValues = MatrixAlgorithms.Solve(system, linearCode.GaloisField); var errorVector = new int[errorLocators.Length]; for (int i = 0, j = 0; i < errorVector.Length; i++) { if (errorLocators[i] == 0) { errorVector[i] = errorVectorValues[j, 0]; j++; } else { errorVector[i] = 0; } } #endregion var rawOriginalMessage = new int[linearCode.K]; for (int i = 0; i < linearCode.K; i++) { rawOriginalMessage[i] = linearCode.GaloisField.AddWords(message.Data[0, i + linearCode.D], errorVector[i + linearCode.D]); } var originalMessage = new MatrixInt(rawOriginalMessage); return(originalMessage); }
public static MatrixInt DecodeAndCorrect(ILinearCode linearCode, MatrixInt message) { if (message.ColumnCount != linearCode.ParityCheckMatrix.ColumnCount) { throw new DimensionMismatchException("Incorrect length of message. Meesage length should be equal number of columns in parity check matrix."); } #region Calculate syndrome var syndrome = MatrixAlgorithms.DotMultiplication(message, linearCode.ParityCheckMatrix.Transpose(), linearCode.GaloisField); #endregion var errorLocations = ErrorLocatorDefault.LocateErrors(linearCode, syndrome); #region Caclulate Error vector var rowCount = linearCode.T; var columnCount = linearCode.T + 1; var system = new int[rowCount, columnCount]; #region Find error positions var errorNumber = 0; for (int errorPosition = 0; errorPosition < linearCode.N; errorPosition++) { if (errorLocations[errorPosition] == 0) { for (int row = 0; row < rowCount; row++) { system[row, errorNumber] = linearCode.ParityCheckMatrix[row, errorPosition]; } errorNumber++; } } for (int i = 0; i < rowCount; i++) { system[i, columnCount - 1] = syndrome[0, i]; } #endregion #region Find error values var weights = MatrixAlgorithms.Solve(new MatrixInt(system), linearCode.GaloisField); #endregion #region Recreate complete error vector var rawErrorVector = new int[linearCode.N]; errorNumber = 0; for (int i = 0; i < linearCode.N; i++) { if (errorLocations[i] == 0) { rawErrorVector[i] = weights.Data[errorNumber, 0]; errorNumber++; continue; } rawErrorVector[i] = 0; } #endregion #endregion var rawOriginalMessage = new int[linearCode.K]; for (int i = 0; i < linearCode.K; i++) { rawOriginalMessage[i] = linearCode.GaloisField.AddWords(message.Data[0, i], rawErrorVector[i]); } var originalMessage = new MatrixInt(rawOriginalMessage); return(originalMessage); }