LDPC (Low Density Parity Check) codes with corresponding parity check matrices selectively constructed with CSI (Cyclic Shifted Identity) and null sub-matrices
View Patent ↗LDPC (Low Density Parity Check) codes with corresponding parity check matrices selectively constructed with CSI (Cyclic Shifted Identity) and null sub-matrices. An LDPC matrix corresponding to an LDPC code is employed within a communication device to encode and/or decode coded signals for use in any of a number of communication systems. The LDPC matrix is composed of a number of sub-matrices and may be partitioned into a left hand side matrix and a right hand side matrix. The right hand side matrix may include two sub-matrix diagonals therein that are composed entirely of CSI (Cyclic Shifted Identity) sub-matrices; one of these two sub-matrix diagonals is located on the center sub-matrix diagonal and the other is located just to the left thereof. All other sub-matrices of the right hand side matrix may be null sub-matrices (i.e., all elements therein are values of zero “0”).
1. An apparatus, comprising:
an input that receives an LDPC (Low Density Parity Check) coded signal; and
an LDPC decoder that employs an LDPC matrix to decode the LDPC coded signal to make an estimate of an information bit encoded therein; and wherein:
the LDPC matrix, composed of a plurality of sub-matrices each having a common size, is partitioned into a left hand side matrix and a right hand side matrix;
each sub-matrix column of the left hand side matrix includes at least a first predetermined number of all zero-valued sub-matrices;
each sub-matrix column of the left hand side matrix includes at most a second predetermined number of CSI (Cyclic Shifted Identity) sub-matrices; and
each sub-matrix within the right hand side matrix is an all zero-valued sub-matrix except those sub-matrices identified below in (a) and (b):
(a) each sub-matrix located on a diagonal of the right hand side matrix is a CSI (Cyclic Shifted Identity) sub-matrix; and
(b) in every row between a second row, which is below and adjacent to a top row, and a bottom row of the right hand side matrix, inclusive, each sub-matrix located on a left hand side of and adjacent to a sub-matrix located on the diagonal of the right hand side matrix is also a CSI sub-matrix.
2. The apparatus of claim 1 , wherein:
each sub-matrix of the left hand side matrix is either an all zero-valued sub-matrix or a CSI sub-matrix.
3. The apparatus of claim 1 , wherein:
one of the plurality of sub-matrices in the left hand side matrix is an identity sub-matrix or a CSI sub-matrix having undergone a cyclic shift of 0 .
4. The apparatus of claim 1 , wherein:
each of the plurality of sub-matrices is a square sub-matrix.
5. The apparatus of claim 1 , wherein:
the right hand side matrix is a square matrix.
6. The apparatus of claim 1 , wherein:
each of the plurality of sub-matrices is a 12×12 square sub-matrix having 12 rows and 12 columns; and
the LDPC matrix includes 12 sub-matrix rows and 48 sub-matrix columns.
7. The apparatus of claim 1 , wherein:
each sub-matrix located on a plurality of diagonals of the left hand side matrix is an all zero-valued sub-matrix;
a first of the plurality of diagonals of the left hand side matrix is adjacent to a second of the plurality of diagonals of the left hand side matrix; and
the second of the plurality of diagonals of the left hand side matrix is adjacent to a third of the plurality of diagonals of the left hand side matrix.
8. The apparatus of claim 1 , wherein each sub-matrix row of the left hand side matrix includes:
a first contiguous plurality of all zero-valued sub-matrices;
a second contiguous plurality of all zero-valued sub-matrices; and
interposed between the first contiguous plurality of all zero-valued sub-matrices and the second contiguous plurality of all zero-valued sub-matrices, at least one additional plurality of sub-matrices that includes at most the second predetermined number of CSI sub-matrices.
9. The apparatus of claim 8 , wherein:
the at least one additional plurality of sub-matrices includes at least one all zero-valued sub-matrix and fewer than the second predetermined number of CSI sub-matrices.
10. The apparatus of claim 1 , wherein:
the left hand side matrix includes a first diagonal sub-matrix band, composed of a plurality of CSI sub-matrices and at least one all zero-valued sub-matrix, located on a first plurality of contiguous diagonals of the left hand side matrix;
the left hand side matrix includes a second diagonal sub-matrix band, composed of all zero-valued sub-matrices, located on a second plurality of contiguous diagonals of the left hand side matrix; and
the first diagonal sub-matrix band is adjacent to the first diagonal sub-matrix band.
11. The apparatus of claim 1 , wherein:
the apparatus is a communication device; and
the communication device is implemented within at least one of a satellite communication system, a wireless communication system, a wired communication system, and a fiber-optic communication system.
12. An apparatus, comprising:
an input that receives an LDPC (Low Density Parity Check) coded signal; and
an LDPC decoder that employs an LDPC matrix to decode the LDPC coded signal to make an estimate of an information bit encoded therein; and wherein:
the LDPC matrix, composed of a plurality of sub-matrices each having a common size, is partitioned into a left hand side matrix and a right hand side matrix;
each sub-matrix column of the left hand side matrix includes at least a first predetermined number of all zero-valued sub-matrices;
each sub-matrix column of the left hand side matrix includes at most a second predetermined number of CSI (Cyclic Shifted Identity) sub-matrices; and
each sub-matrix within the right hand side matrix is an all zero-valued sub-matrix except those sub-matrices identified below in (a) and (b):
(a) each sub-matrix located on a diagonal of the right hand side matrix is a CSI (Cyclic Shifted Identity) sub-matrix; and
(b) in every row between a second row, which is below and adjacent to a top row, and a bottom row of the right hand side matrix, inclusive, each sub-matrix located on a left hand side of and adjacent to a sub-matrix located on the diagonal of the right hand side matrix is also a CSI sub-matrix;
each sub-matrix located on a plurality of diagonals of the left hand side matrix is an all zero-valued sub-matrix;
a first of the plurality of diagonals of the left hand side matrix is adjacent to a second of the plurality of diagonals of the left hand side matrix;
the second of the plurality of diagonals of the left hand side matrix is adjacent to a third of the plurality of diagonals of the left hand side matrix;
each of the plurality of sub-matrices is a square sub-matrix; and
the right hand side matrix is a square matrix.
13. The apparatus of claim 12 , wherein:
one of the plurality of sub-matrices in the left hand side matrix is an identity sub-matrix or a CSI sub-matrix having undergone a cyclic shift of 0.
14. The apparatus of claim 12 , wherein:
each of the plurality of sub-matrices is a 12×12 square sub-matrix having 12 rows and 12 columns; and
the LDPC matrix includes 12 sub-matrix rows and 48 sub-matrix columns.
15. The apparatus of claim 12 , wherein:
the left hand side matrix includes a first diagonal sub-matrix band, composed of a plurality of CSI sub-matrices and at least one all zero-valued sub-matrix, located on a first plurality of contiguous diagonals of the left hand side matrix;
the left hand side matrix includes a second diagonal sub-matrix band, composed of all zero-valued sub-matrices, located on a second plurality of contiguous diagonals of the left hand side matrix; and
the first diagonal sub-matrix band is adjacent to the first diagonal sub-matrix band.
16. The apparatus of claim 12 , wherein:
the apparatus is a communication device; and
the communication device is implemented within at least one of a satellite communication system, a wireless communication system, a wired communication system, and a fiber-optic communication system.
17. An apparatus, comprising:
an input that receives an LDPC (Low Density Parity Check) coded signal; and
an LDPC decoder that employs an LDPC matrix to decode the LDPC coded signal to make an estimate of an information bit encoded therein; and wherein:
the LDPC matrix, composed of a plurality of sub-matrices each having a common size, is partitioned into a left hand side matrix and a right hand side matrix;
each sub-matrix column of the left hand side matrix includes at least a first predetermined number of all zero-valued sub-matrices;
each sub-matrix column of the left hand side matrix includes at most a second predetermined number of CSI (Cyclic Shifted Identity) sub-matrices; and
each sub-matrix within the right hand side matrix is an all zero-valued sub-matrix except those sub-matrices identified below in (a) and (b):
(a) each sub-matrix located on a diagonal of the right hand side matrix is a CSI (Cyclic Shifted Identity) sub-matrix; and
(b) in every row between a second row, which is below and adjacent to a top row, and a bottom row of the right hand side matrix, inclusive, each sub-matrix located on a left hand side of and adjacent to a sub-matrix located on the diagonal of the right hand side matrix is also a CSI sub-matrix;
the left hand side matrix includes a first diagonal sub-matrix band, composed of a plurality of CSI sub-matrices and at least one all zero-valued sub-matrix, located on a first plurality of contiguous diagonals of the left hand side matrix;
the left hand side matrix includes a second diagonal sub-matrix band, composed of all zero-valued sub-matrices, located on a second plurality of contiguous diagonals of the left hand side matrix; and
the first diagonal sub-matrix band is adjacent to the first diagonal sub-matrix band.
18. The apparatus of claim 17 , wherein:
each of the plurality of sub-matrices is a 12×12 square sub-matrix having 12 rows and 12 columns; and
the LDPC matrix includes 12 sub-matrix rows and 48 sub-matrix columns.
19. The apparatus of claim 17 , wherein each sub-matrix row of the left hand side matrix includes:
a first contiguous plurality of all zero-valued sub-matrices;
a second contiguous plurality of all zero-valued sub-matrices; and
interposed between the first contiguous plurality of all zero-valued sub-matrices and the second contiguous plurality of all zero-valued sub-matrices, at least one additional plurality of sub-matrices that includes at most the second predetermined number of CSI sub-matrices.
20. The apparatus of claim 17 , wherein:
the apparatus is a communication device; and
the communication device is implemented within at least one of a satellite communication system, a wireless communication system, a wired communication system, and a fiber-optic communication system.