/// <summary>
/// Create a Vandermonde matrix of size row x column over GF16
/// </summary>
/// <remarks>
/// The Vandermonde matrix is typically used to create the encoding matrix where:
/// - The number of Columns of the matrix correspond to number of checksum
/// packets.
/// - The number of Rows of the matrix correspond to number of data packets.
/// </remarks>
/// <param name="columns">The number of columns of the Vandermonde matrix</param>
/// <param name="rows">The number of rows of the Vandermode matrix</param>
/// <returns></returns>
public static UInt16[,] CreateVandermondeMatrix(int columns, int rows)
{
// TODO: Add input validation
// maxChecksumPackets will be the max number of Columns of the encoding static matrix
// maxDataPackets will be the max number of Rows of the encoding static matrix
UInt16[,] vandermondeMtx = new UInt16[columns, rows];
// Creation of the Vandermonde Matrix over GF16 with the following
// (2^column)^row
// As an example, a 5 x 3 Vandermonde Matrix over GF16 (5 data packets, 3 checksum packets)
// would give the following:
//
// 1^0 2^0 4^0
// 1^1 2^1 4^1
// 1^2 2^2 4^2
// 1^3 2^3 4^3
// 1^4 2^4 4^4
//
// Which gives:
//
// 1 1 1
// 1 2 4
// 1 4 16
// 1 8 64
// 1 16 256
for (int col = 0; col < columns; col++)
{
// multFactor is the number to multiply to get the value in the next row
// for a given column of the Vandermonde matrix
UInt16 multFactor = GF16.Power(2, (uint)col);
for (int row = 0; row < rows; row++)
{
if (row == 0)
{
// Special case the first row (power of zero)
vandermondeMtx[col, row] = 1;
}
else
{
// Each element of the Vandermonde matrix is calculated as (2^column)^row over GF16
// This algorithm uses the previous row to compute the next one to improve
// the performances (instead of recalculating (2^column)^row)
vandermondeMtx[col, row] = GF16.Multiply(vandermondeMtx[col, row - 1], multFactor);
}
}
}
return(vandermondeMtx);
}
/// <summary>
/// Create the decoding matrix
/// </summary>
/// <param name="nbDataPackets">Number of data packet</param>
/// <param name="nbChecksumPackets">Number of checksum packet</param>
/// <param name="rtpPackets">Array of rtpPackets</param>
/// <returns>The decoding matrix</returns>
/// <example>
/// For example, if you have 3 data packets and 2 checksum
/// packets and get the last data packet, you will get
/// the following matrix
/// 0 1 1
/// 0 1 2
/// 1 1 4
/// </example>
// TODO: To be more generic, we should use System.Array instead of array of BufferChunks
public static GF16[,] DecodingMatrixGeneration(BufferChunk[] dataReceived, int nbChecksumPackets)
{
// nbTotalPackets is the total # rtpPackets to create (data packets and checksum packets)
int nbTotalPackets = dataReceived.Length;
int nbDataPackets = nbTotalPackets - nbChecksumPackets;
// Let's suppose that we lost the 2 first packets
// So [E'] that should have been
// 1 0 0 1 1
// 0 1 0 1 2
// 0 0 1 1 4
// is actually
// 0 1 1
// 0 1 2
// 1 1 4
// The reverted decoding matrix will be multiplied by data received to get all the datas
// for instance [D0..D2] = [D2 C0 C1] x 1/[E']
// => So the number of columns should correspond to the number of data recieved + checksum received
// and the number of rows should correspond of the number of data packet K
// count the number of packets received
int nbPacketsReceived = ReceivedPacketsCount(nbTotalPackets, dataReceived);
// nbPacketsReceived columns, K rows
// Note that the # columns is smaller than the number of packet received
// in case the number of packet lost was smaller than the number than
// the number of checksum packets (we short the matrix: It's like if we lost the last
// checksum(s) packet(s)
GF16[,] mtxEprime_GF16 = new GF16[nbPacketsReceived, nbDataPackets];
// Construct the matrix mtxEprime_GF16 from the rtpPackets received
// Note see also Jay's Decode method
// Loop trough the data rtpPackets and put a 1 on the row of the packet
// received
int foundIndex = 0;
for (int index = 0; index < nbDataPackets; index++)
{
if (dataReceived[index] != null) // not a packet lost
{
// Generate a row in the mtxEprime_GF16 (decode matrix)
if (index < nbDataPackets)
{
// TODO: To be clean, we should have initialized all the other items
// on the row explicitely to zero or make sure their are set them to zero
// when creating the new matrix
mtxEprime_GF16[foundIndex, index] = (UInt16)1;
}
foundIndex++;
// if (foundIndex >= nbPacketsReceived-nbAdditionalPacketsReceived)
// return mtxEprime_GF16;
}
}
// Generate a Vandermonde Mtx for the other items
// TODO: Change that to use the Vandermonde static mtx
for (UInt32 m = 0; m < nbChecksumPackets; m++)
{
// Note: If a checksum packet has been lost, the column is skiped
if (dataReceived[m + nbDataPackets] != null) // not a packet lost
{
for (UInt32 k = 0; k < nbDataPackets; k++)
{
// Each element of the Vandermonde matrix is calculated as (m+1)^k over GF16
// mtx[column, row] = (column+1)^row
// With Vandermonde: 1^x, 2^x, 3^x, ... the code was:
// mtxEprime_GF16[foundIndex, k] = GF16.Power((UInt16)(m+1), (UInt32)k);
// I experimented problems (no pivot found during invertion of Eprime)
// when losing 3 packets (worked fine when losing 2 packets)
// So I changed, to use Vandermonde matrix were mtx[column, row] = (2^column)^row
mtxEprime_GF16[foundIndex, k] = GF16.Power((UInt16)GF16.Power(2, (m)), (UInt32)k);
// TODO: Check if Jay's approach is more efficient: mtxE_GF16[m, k] = GF16.gf_exp[GF16.Modnn(k*m)];
}
foundIndex++;
// if (foundIndex >= nbPacketsReceived-nbAdditionalPacketsReceived)
// return mtxEprime_GF16;
}
} // for
return(mtxEprime_GF16);
}