LDPC CODE MATRICES
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 - 57 . (canceled)
58 . A system 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.
59 . The system of claim 58 , wherein the first number is greater than or equal to 48 and less than or equal to 100.
60 . The system of claim 58 , wherein the second number is greater than or equal to 34 and less than or equal to 43.
61 . The system of claim 58 , wherein the third number is greater than or equal to 5 and less than or equal to 7.
62 . The system of claim 58 , wherein the code word is communicated according to a Media over Coax Alliance (MoCA) specification.
63 . The system of claim 58 , wherein two or more columns of the parity portion have 4 positive elements.
64 . The system of claim 58 , wherein two or more columns of the parity portion have 5 positive elements.
65 . A method 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.
66 . The method of claim 65 , wherein the first number is greater than or equal to 48 and less than or equal to 100.
67 . The method of claim 65 , wherein the second number is greater than or equal to 34 and less than or equal to 43.
68 . The method of claim 65 , wherein the third number is greater than or equal to 5 and less than or equal to 7.
69 . The method of claim 65 , wherein the code word is communicated according to a Media over Coax Alliance (MoCA) specification.
70 . The method of claim 65 , wherein two or more columns of the parity portion have 4 positive elements.
71 . The method of claim 65 , wherein two or more columns of the parity portion have 5 positive elements.
72 . A system 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.
73 . The system of claim 72 , wherein the first number is greater than or equal to 48 and less than or equal to 100.
74 . The system of claim 72 , wherein the second number is greater than or equal to 34 and less than or equal to 43.
75 . The system of claim 72 , wherein the third number is greater than or equal to 5 and less than or equal to 7.
76 . The system of claim 72 , wherein the code word is communicated according to a Media over Coax Alliance (MoCA) specification.
77 . The system of claim 72 , wherein the code word is communicated to a smart phone.