Ldpc code matrices

A system comprising:

• a hardware processor operable to encode data according to a Low Density Parity Check (LDPC) matrix, the encoded data corresponding to a code word comprising a payload and a parity, the LDPC matrix comprising a plurality of elements of a systematic matrix and a plurality of elements of a parity matrix, wherein:
• the length of the payload is the product (“XY”) of a first number (“X”) and a second number (“Y”),
• the length of the parity is the product (“XZ”) of X and a third number (“Z”),
• 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 matrix and the plurality of elements in the parity matrix 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.

A method comprising:

• encoding data, in a hardware processor, according to a Low Density Parity Check (LDPC) matrix, the encoded data corresponding to a code word comprising a payload and a parity, the LDPC matrix comprising a plurality of elements of a systematic matrix and a plurality of elements of a parity matrix;
• and
• communicating the encoded data according to a Media over Coax Alliance (MoCA) specification, wherein
• the length of the payload is the product (“XY”) of a first number (“X”) and a second number (“Y”),
• the length of the parity is the product (“XZ”) of X and a third number (“Z”),
• 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 matrix and the plurality of elements in the parity matrix 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.