Systems and methods for generating optimized combination sets for error correction in data transmission

A system comprising:

• a matrix-generating device comprising:
• processing circuitry, to:
• generate a first matrix;
• perform an incident cycle optimization process using the first matrix to generate a modified first matrix which has fewer incident cycles than the first matrix;
• perform an encoder gate optimization process using the modified first matrix to generate a further modified first matrix, wherein fewer encoder gates are needed to encode data using the further modified first matrix than when using the modified first matrix;
• generate a second matrix, wherein the further modified first matrix is a submatrix of the second matrix;
• perform the incident cycle optimization process using the second matrix to generate a modified second matrix which has fewer incident cycles than the second matrix;
• perform the encoder gate optimization process using each of the further modified first matrix and the modified second matrix to generate a further modified second matrix, wherein fewer encoder gates are needed to encode data using the further modified second matrix than when using the modified second matrix;
• and
• configure a transmitting device, which is communicatively coupled to the system, using the further modified first matrix and the further modified second matrix, wherein the transmitting device is configured to:
• receive transmission data;
• encode the transmission data using one of the further modified first matrix and the further modified second matrix;
• and
• transmit the encoded transmission data over a channel.

A non-transitory computer-readable medium having non-transitory computer-readable instructions encoded thereon that, when executed by processing circuitry, cause the processing circuitry to:

• generate a first matrix;
• perform an incident cycle optimization process using the first matrix to generate a modified first matrix which has fewer incident cycles than the first matrix;
• perform an encoder gate optimization process using the modified first matrix to generate a further modified first matrix, wherein fewer encoder gates are needed to encode data using the further modified first matrix than when using the modified first matrix;
• generate a second matrix, wherein the further modified first matrix is a submatrix of the second matrix;
• perform the incident cycle optimization process using the second matrix to generate a modified second matrix which has fewer incident cycles than the second matrix;
• perform the encoder gate optimization process using each of the further modified first matrix and the modified second matrix to generate a further modified second matrix, wherein fewer encoder gates are needed to encode data using the further modified second matrix than when using the modified second matrix;
• and
• configure a transmitting device using the further modified first matrix and the further modified second matrix, wherein the transmitting device is configured to:
• receive transmission data;
• encode the transmission data using one of the further modified first matrix and the further modified second matrix;
• and
• transmit the encoded transmission data over a channel.

A method for data transmission, the method comprising:

• receiving transmission data;
• encoding the transmission data using one of a further modified first matrix and a further modified second matrix, wherein the further modified first matrix and the further modified second matrix are generated by:
• generating, by processing circuitry, a first matrix;
• performing, by the processing circuitry, an incident cycle optimization process using the first matrix to generate a modified first matrix which has fewer incident cycles than the first matrix;
• performing, by the processing circuitry, an encoder gate optimization process using the modified first matrix to generate the further modified first matrix, wherein fewer encoder gates are needed to encode data using the further modified first matrix than when using the modified first matrix;
• generating, by the processing circuitry, a second matrix, wherein the further modified first matrix is a submatrix of the second matrix;
• performing, by the processing circuitry, the incident cycle optimization process using the second matrix to generate a modified second matrix which has fewer incident cycles than the second matrix;
• and
• performing, by the processing circuitry, the encoder gate optimization process using each of the further modified first matrix and the modified second matrix to generate the further modified second matrix, wherein fewer encoder gates are needed to encode data using the further modified second matrix than when using the modified second matrix;
• and
• transmitting the encoded transmission data over a channel.