Encoding and decoding techniques using low-density parity check codes

A method comprising:

• receiving message information;
• generating a portion of parity information based on a first equation calculated from at least an inverse of a first sub-matrix in a first portion of a matrix, the first sub-matrix including a diagonal entry having a value of one;
• generating an additional portion of the parity information based on a second equation calculated from at least a triangular sub-matrix in a second portion of the matrix;
• and
• generating codewords based at least in part on the portion of the parity information and the additional portion of the parity information.

A method comprising:

• generating a first matrix from a parity check matrix of a low-density parity check code, the first matrix having a triangular sub-matrix in a first portion of the first matrix;
• generating parity information to encode message information based at least in part on the first matrix if a total number of rows of the triangular sub-matrix is equal to a rank of the parity check matrix;
• and
• if the total number of rows of the first triangular sub-matrix is less than the rank of the parity check matrix, performing a triangularization operation on a second sub-matrix in a second portion of the first matrix to generate a second matrix, and generating parity information to encode the message information based at least in part on the second matrix.

A method comprising:

• performing a first triangularization operation on parity check matrix of a low-density parity check code to generate a first matrix having a triangular sub-matrix in a first portion of the first matrix, the triangular sub-matrix having a total number of rows less than a rank of the parity check matrix;
• performing a second triangularization operation on at least a portion of a sub-matrix in a second portion of the first matrix such that at least one row of the first matrix includes all zeros entries;
• removing the at least one row of the first matrix that includes all zeros entries to generate a second matrix, wherein at least one of performing the first triangularization, performing the first triangularization, and removing the at least one row of the first matrix is performed by an electronic unit;
• and
• calculating at least one equation to generate at least a portion of parity information based at least in part on the second matrix.

An apparatus comprising:

• an input to receive message information;
• an encoder to generate codewords having the message information and parity information, and to generate the parity information based on an equation calculated from a combination of at least an inverse of a triangular sub-matrix generated from a first portion of a parity check matrix of a low-density parity check code and a sub-matrix generated from a second portion of the parity check matrix;
• and
• an output to provide the codewords.

An apparatus comprising:

• an input to receive message information;
• and
• a module to generate codewords having the message information and parity information, the module configured to generate a portion of the parity information based on a first equation calculated from at least an inverse of a first sub-matrix in a first portion of a matrix, the first sub-matrix including a diagonal entry having a value of one, the module also configured to generate an additional portion of the parity information based on a second equation calculated from at least a triangular sub-matrix in a second portion of the matrix;
• and
• an output to provide the codewords.

A computer-readable storage medium comprising instructions, which when implemented by one or more processors perform the following operations:

• generate a first matrix from a parity check matrix of a low-density parity check code, the first matrix having a triangular sub-matrix in a first portion of the first matrix;
• generate parity information to encode message information based at least in part on the first matrix if a total number of rows of the triangular sub-matrix is equal to the rank of the parity check matrix;
• and
• if the total number of rows of the triangular sub-matrix is less than the rank of the parity check matrix, perform a triangularization operation on a second sub-matrix in a second portion of the first matrix to generate a second matrix, and generate parity information to encode the message information based at least in part on the second matrix.