LDPC code matrices
An LDPC parity check matrix, includes a systematic portion having a plurality of systematic elements having a value, the value each systematic element determining a cyclic shift to be applied to rows of an identity submatrix corresponding to that element; and a parity portion having a plurality of panty elements having a value, the value of each parity element determining a cyclic shift to be applied to rows of an identity submatrix corresponding to that element; wherein the weights of each column of a group of columns of the parity portion is the same. The LDPC parity check matrix may be used for data access, communication and storage, and may be used, for example for communications among a plurality of network nodes.
1. A network node comprising:
a digital data transmitter comprising a hardware processor operable to encode data as a code word according to a Low Density Parity Check (LDPC) matrix, wherein:
the LDPC matrix relates a payload of the code word with a parity to enable a reduction in a number of decoding iterations required by a decoder that receives the code word,
the LDPC matrix comprises a plurality of elements of a systematic portion and a plurality of elements of a parity portion,
the length of the payload is the product (“XY”) of a first number (“X”, a positive integer) and a second number (“Y”, a positive integer),
the length of the parity is the product (“XZ”) of X and a third number (“Z, a positive integer),
the number of elements of the systematic portion is the product (“YZ”) of Y and Z,
the number of elements of the parity portion is the product (“ZZ”) of Z and Z,
each element of the plurality of elements in the systematic portion and the plurality of elements in the parity portion correspond to a submatrix having X columns and X rows,
a zero-valued element corresponds to an identity submatrix,
a positive-valued element corresponds to an identity submatrix with rows that are a cyclically shifted according the positive value, and
a negative-valued systematic element corresponds to a zero submatrix, and
two or more columns of the parity portion have an equal number of positive-valued elements.
2. The system of claim 1 , wherein the first number is greater than or equal to 48 and less than or equal to 100.
3. The system of claim 1 , wherein the second number is greater than or equal to 34 and less than or equal to 43.
4. The system of claim 1 , wherein the third number is greater than or equal to 5 and less than or equal to 7.
5. The system of claim 1 , wherein the code word is communicated according to a Media over Coax Alliance (MoCA) specification.
6. The system of claim 1 , wherein two or more columns of the parity portion have 4 positive elements.
7. The system of claim 1 , wherein two or more columns of the parity portion have 5 positive elements.
8. A method for operating a network node comprising:
encoding data as a code word, using a digital data transmitter comprising a hardware processor, according to a Low Density Parity Check (LDPC) matrix, wherein:
the LDPC matrix relates a payload of the code word with a parity to enable a reduction in a number of decoding iterations required by a decoder that receives the code word,
the LDPC matrix comprises a plurality of elements of a systematic portion and a plurality of elements of a parity portion,
the length of the payload is the product (“XY”) of a first number (“X”, a positive integer) and a second number (“Y”, a positive integer),
the length of the parity is the product (“XZ”) of X and a third number (“Z, a positive integer),
the number of elements of the systematic portion is the product (“YZ”) of Y and Z,
the number of elements of the parity portion is the product (“ZZ”) of Z and Z,
each element of the plurality of elements in the systematic portion and the plurality of elements in the parity portion correspond to a submatrix having X columns and X rows,
a zero-valued element corresponds to an identity submatrix,
a positive-valued element corresponds to an identity submatrix with rows that are a cyclically shifted according the positive value, and
a negative-valued systematic element corresponds to a zero submatrix, and
two or more columns of the parity portion have an equal number of positive-valued elements.
9. The method of claim 8 , wherein the first number is greater than or equal to 48 and less than or equal to 100.
10. The method of claim 8 , wherein the second number is greater than or equal to 34 and less than or equal to 43.
11. The method of claim 8 , wherein the third number is greater than or equal to 5 and less than or equal to 7.
12. The method of claim 8 , wherein the code word is communicated according to a Media over Coax Alliance (MoCA) specification.
13. The method of claim 8 , wherein two or more columns of the parity portion have 4 positive elements.
14. The method of claim 8 , wherein two or more columns of the parity portion have 5 positive elements.
15. A network node comprising:
a wireless communication device operable to encode data as a code word according to a Low Density Parity Check (LDPC) matrix, wherein:
the LDPC matrix relates a payload of the code word with a parity to enable a reduction in a number of decoding iterations required by a decoder that receives the code word,
the LDPC matrix comprises a plurality of elements of a systematic portion and a plurality of elements of a parity portion,
the length of the payload is the product (“XY”) of a first number (“X”, a positive integer) and a second number (“Y”, a positive integer),
the length of the parity is the product (“XZ”) of X and a third number (“Z, a positive integer),
the number of elements of the systematic portion is the product (“YZ”) of Y and Z,
the number of elements of the parity portion is the product (“ZZ”) of Z and Z,
each element of the plurality of elements in the systematic portion and the plurality of elements in the parity portion correspond to a submatrix having X columns and X rows,
a zero-valued element corresponds to an identity submatrix,
a positive-valued element corresponds to an identity submatrix with rows that are a cyclically shifted according the positive value, and
a negative-valued systematic element corresponds to a zero submatrix, and
two or more columns of the parity portion have an equal number of positive-valued elements.
16. The system of claim 15 , wherein the first number is greater than or equal to 48 and less than or equal to 100.
17. The system of claim 15 , wherein the second number is greater than or equal to 34 and less than or equal to 43.
18. The system of claim 15 , wherein the third number is greater than or equal to 5 and less than or equal to 7.
19. The system of claim 15 , wherein the code word is communicated according to a Media over Coax Alliance (MoCA) specification.
20. The system of claim 15 , wherein the code word is communicated to a smart phone.