Multi-rate LDPC code system and method

A communications system which uses LDPC and comprises permutation matrices P of size Z×Z comprising a plurality of matrices P(0) . . . P(Z−1) and a stairs matrix P(st), from which a block parity check matrix Hb is constructed, using only the permutation matrices P:

• P(0) . . . P(Z−1), the stairs matrix P(st) and a zero matrix 0, wherein the initial dimensions of Hb are:
• 0.5 Nm×Nm or 0.5 n×n, wherein n is an integer representing a codeword vector length, wherein the height of the block parity check matrix Hb is half of its width and wherein the initial code rate represented by the block parity check matrix Hb is:
• R=(n−k)/n=0.5, wherein the initial dimensions of the block parity check matrix Hb are referenced by the Z×Z matrices, and denoted by Mb ×Nb, and is such to satisfy the following:
• a. The Mb ×Mb right side of the matrix is lower triangular;
• b. The lower rightmost block of the matrix is P(st)=Pst;
• c. Each row in the block matrix contains 6 or 7 non-zero block entries belonging to different sets of columns;
• d. Hb is an irregular matrix, such that the block columns weights spectrum is optimized for providing good code performance in a small number of decoding iterations (ablock column's weidght is the number of non-zero block entries in a column);
• e. Rows j and j+Mb/2 for j=1 . . . Mb/2 have non-overlapping non-zero block entries;
• wherein a method for deriving a plurality of codes of various rates from a mother code is implemented by summing up pairs of rows of the block matrix Hb creating an H or Hm matrix, as follows:
• 1. Decide the required code rate:
• R
• =
• 1
• 2
• +
• α
• N
• b
• for any
• α
• ∈
• {
• 0
• ,
• …
• ⁢
• ,
• N
• b
• 4
• }
• ;
• 2. Repeat summing up the rows j and
• j
• +
• M
• b
• 2
• for j =1,. . . , α;
• 3. The resulting block matrix after summation is a (Mbα)×Nb, hence the code rate is
• 1
• -
• M
• b
• -
• α
• N
• b
• =
• 1
• 2
• +
• α
• N
• b
• ;
• wherein the constructed mother code or the resulting matrix after summation remains a block matrix with permutation blocks as its entries and wherein said plurality of derived codes are of length Nm with the same number of 1′s in their parity-check matrix.

A communications system which uses LDPC and comprises permutation matrices P of size Z×Z comprising a plurality of matrices P(0) . . . P(Z−1) and a stairs matrix P(st), from which a block parity check matrix Hb is constructed, using only the permutation matrices P:

• P(0) . . . P(Z−1), the stairs matrix P(st) and a zero matrix 0, wherein the initial dimensions of Hb are:
• 0.5 Nm×Nm or 0.5 n×n, wherein n is an integer representing a codeword vector length, wherein the height of the block parity check matrix Hb is half of its width and wherein the initial code rate represented by the block parity check matrix Hb is:
• R=(n−k)/n=0.5, wherein the initial dimensions of the block parity check matrix Hb are referenced by the Z×Z matrices, and denoted by Mb ×Nb, and is such to satisfy the following:
• a. The Mb ×Mb right side of the matrix is lower triangular;
• b. The lower rightmost block of the matrix is P(st)=Pst;
• c. Each row in the block matrix contains 6 or 7 non-zero block entries belonging to different sets of columns;
• d. Hb is an irregular matrix, such that the block columns weights spectrum is optimized for providing good code performance in a small number of decoding iterations (ablock column's weidght is the number of non-zero block entries in a column);
• e. Rows j and j+Mb/2 for j=1 . . . Mb/2 have non-overlapping non-zero block entries;
• wherein four mother codes of lengths Nm=2304, 1728, 1152, 576 are used, with Z=12, Z=24 or other Z multiples of 48 bits to accommodate an integer number of OFDMA sub-channels.