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);
}
