/// <summary>
/// Decodes vector using Fast Hadamard Transform.
/// 0s in the vector are changed to '-1', then the encoded vector is multiplied with H matrixes and the results
/// and summed up together. The index of the highest absolute value in the sum vector is used for decoding.
/// Index value is transformed to reversed binary number with '1' in front of it the highest value
/// was positive and '0' if it was negative. The final vector is the decoded vector.
/// </summary>
/// <param name="vector">Encoded vector</param>
/// <param name="m">Code parameter m</param>
/// <returns>Decoded vector</returns>
public static Vector DecodeSingleVector(Vector vector, int m)
{
var transformedVector = vector.TranformBitsFromZeroToMinusOne();
// Multiply vector with H matrixes and sum up the results to a single vector
for (int i = 1; i <= m; i++)
{
var calculationMatrix = HadamardTransformMatrix.GetTransformMatrix(i, m);
transformedVector = MatrixUtils.MutltiplyVectorWithMatrix(transformedVector, calculationMatrix, Convert.ToInt32(Math.Pow(2, m)));
}
// Get the index of the highest absolute value in the vector and convert it to binary representation
var vectorDataAbsValues = transformedVector.Data.Select(x => Math.Abs(x)).ToList();
var maxPosition = vectorDataAbsValues.IndexOf(vectorDataAbsValues.Max());
var reversedBinaryValue = Convert.ToString(maxPosition, 2);
var zerosToAddCount = m - reversedBinaryValue.Length;
if (zerosToAddCount != 0)
{
reversedBinaryValue = new string('0', zerosToAddCount) + reversedBinaryValue;
}
// Add the first digit, based on if the highest value was positive or negative
reversedBinaryValue += transformedVector.Data[maxPosition] < 0 ? '0' : '1';
var binaryValue = reversedBinaryValue.ToCharArray();
Array.Reverse(binaryValue);
var decodedVectorData = ConversionUtils.ConvertStringToIntegerArray(new string(binaryValue));
return(new Vector(decodedVectorData));
}
/// <summary>
/// Clear old matrixes and calculate generator and identity matrixes before launching next view.
/// </summary>
private void ContinueBtn_Click(object sender, EventArgs e)
{
var m = decimal.ToInt32(mValue.Value);
GeneratorMatrix.PrepareMatrixes(m);
HadamardTransformMatrix.PrepareHadamardTransformMatrixes(m);
new MainView(this, m).Show();
Hide();
}
