LDPC code matrices
View Patent ↗An LDPC parity check matrix includes a systematic portion having a plurality of systematic elements and a parity portion having a plurality of parity elements. The value of each systematic element determines a cyclic shift to be applied to rows of an identity submatrix corresponding to that element. The value of each parity element determines a cyclic shift to be applied to rows of an identity submatrix corresponding to that element. The weights of two or more columns of the parity portion are the same.
1. A system comprising:
a digital data transmitter comprising a hardware processor operable to encode data according to a Low Density Parity Check (LDPC) matrix, wherein:
the encoded data corresponds to a code word comprising a payload and a parity,
the LDPC matrix is configured to relate the payload with the 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 48.
3. The system of claim 1 , wherein the first number is 80.
4. The system of claim 1 , wherein the first number is 100.
5. The system of claim 1 , wherein the second number is 34.
6. The system of claim 1 , wherein the second number is 39.
7. The system of claim 1 , wherein the second number is 41.
8. The system of claim 1 , wherein the second number is 43.
9. The system of claim 1 , wherein the third number is 5.
10. The system of claim 1 , wherein the third number is 6.
11. The system of claim 1 , wherein the third number is 7.
12. The system of claim 1 , wherein the encoded data is communicated according to a Media over Coax Alliance (MoCA) specification.
13. The system of claim 1 , wherein two or more columns of the parity portion have 4 positive elements.
14. The system of claim 1 , wherein two or more columns of the parity portion have 5 positive elements.
15. A method comprising:
encoding data, in a hardware processor of a digital data transmitter, according to a Low Density Parity Check (LDPC) matrix, wherein:
the encoded data corresponds to a code word comprising a payload and a parity,
the LDPC matrix is configured to relate the payload with the parity to enable a reduction in a number of decoding iterations required by a decoder, and
the LDPC matrix comprises a plurality of elements of a systematic portion and a plurality of elements of a parity portion; and
communicating the encoded data to the decoder according to a Media over Coax Alliance (MoCA) specification, wherein:
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 method of claim 15 , wherein the first number is 48.
17. The method of claim 15 , wherein the first number is 80.
18. The method of claim 15 , wherein the first number is 100.
19. The method of claim 15 , wherein the second number is 34.
20. The method of claim 15 , wherein the second number is 39.
21. The method of claim 15 , wherein the second number is 41.
22. The method of claim 15 , wherein the second number is 43.
23. The method of claim 15 , wherein the third number is 5.
24. The method of claim 15 , wherein the third number is 6.
25. The method of claim 15 , wherein the third number is 7.
26. The method of claim 15 , wherein two or more columns of the parity portion have 4 positive elements.
27. The method of claim 15 , wherein two or more columns of the parity portion have 5 positive elements.