Examples of check codes, methods of creating check codes, and communication systems utilizing check codes, such as low-density parity-check codes (LDPC codes) are described herein. In some examples, check codes described herein utilize a larger number of check operations than check bits.

Apparatuses and methods for performing an error correction code (ECC) operation are provided. One example method can include encoding data by including parity data for a number of cross-over bits, wherein the number of cross-over bits are bits located at intersections of column codewords and row codewords.

A memory system includes a packet protection circuit. The packet protection circuit includes a plurality of first CRC calculation circuits, each configured to calculate a CRC of M-byte data, where M is an integer greater than or equal to 1 and less than N, where N is an integer greater than or equal to 2, a first selector configured to output a CRC calculation result of one of the first CRC calculation circuits, and a second CRC calculation circuit configured to calculate a CRC of L-byte data, where L<N, where L=NZ, and Z is an integer greater than 1, and add the CRC of L-byte data to the CRC calculation result output from the first selector to generate a first CRC that is compared with a second CRC to detect an error in a data packet transmitted between the host interface unit and the host device.

Apparatuses and methods for performing an error correction code (ECC) operation are provided. One example method can include encoding data by including parity data for a number of cross-over bits, wherein the number of cross-over bits are bits located at intersections of column codewords and row codewords.

One embodiment facilitates data placement in a storage device. During operation, the system receives chunks of data to be written to a non-volatile memory. The system encodes a first chunk based on a first error-correcting code (ECC) to obtain a first ECC-encoded codeword. The system encodes a first group of ECC-encoded codewords which include the first ECC-encoded codeword, based on an erasure code (EC) to obtain a first EC-encoded group, wherein a respective EC-encoded group includes EC parity bits. The system encodes the EC parity bits of the obtained first EC-encoded group based on a second error-correcting code (ECC) to obtain ECC-encoded EC parity bits. The system writes the first EC-encoded group and the ECC-encoded EC parity bits to the non-volatile memory.

In a coding device (20), a first coding unit (21) generates a parity of an RS code by coding, based on the RS code, each first data sequence existing in a direction different from a row direction of input data, and generates coded data by attaching the parity of the RS code to each first data sequence, thereby consequently expanding a matrix. A second coding unit (22) generates a parity of a BCH code and a parity of an LDPC code by coding, based on the BCH code and the LDPC code, each second data sequence existing in a row direction of the coded data, and generates a plurality of DVB-S2 frames (13) including, per DVB-S2 frame (13), one data sequence existing in the row direction of the coded data, the corresponding parity of the BCH code, and the corresponding parity of the LDPC code.

One embodiment facilitates data placement in a storage device. During operation, the system receives chunks of data to be written to a non-volatile memory. The system encodes a first chunk based on a first error-correcting code (ECC) to obtain a first ECC-encoded codeword. The system encodes a first group of ECC-encoded codewords which include the first ECC-encoded codeword, based on an erasure code (EC) to obtain a first EC-encoded group, wherein a respective EC-encoded group includes EC parity bits. The system encodes the EC parity bits of the obtained first EC-encoded group based on a second error-correcting code (ECC) to obtain ECC-encoded EC parity bits. The system writes the first EC-encoded group and the ECC-encoded EC parity bits to the non-volatile memory.

In one embodiment, a computer program product includes a computer readable storage medium having program instructions embodied therewith. The computer readable storage medium is not a transitory signal per se. The embodied program instructions are readable/executable by a processor to cause the processor to write, by the processor, data to a storage medium of a data storage system using a partial reverse concatenated modulation code. The partial reverse concatenated modulation code includes encoding the data by applying a C2 encoding scheme prior to encoding the data by applying one or more modulation encoding schemes, followed by encoding the data by applying a C1 encoding scheme subsequent to the encoding of the data with the one or more modulation encoding schemes. Other computer program products for writing data to a storage medium of a data storage system using a partial reverse concatenated modulation code are presented according to more embodiments.

In one embodiment, a system includes a processor, and logic integrated with the processor, executable by the processor, or integrated with and executable by the processor. The logic is configured to cause the processor to write, by the processor, data to a storage medium of a data storage system using a partial reverse concatenated modulation code. The partial reverse concatenated modulation code comprises encoding the data by applying a C2 encoding scheme prior to encoding the data by applying one or more modulation encoding schemes, followed by encoding the data by applying a C1 encoding scheme subsequent to the encoding of the data with the one or more modulation encoding schemes.

Embodiments relate to correcting erasures in a storage array. An aspect includes dividing data into a plurality of stripes for storage in a storage array comprising a plurality of storage locations, each stripe comprising M rows and N columns, each of the M rows including a number r of row parities, wherein r is greater than zero. Another aspect includes dividing each stripe into two or more column sets, each column set comprising a respective set of one or more columns of the stripe. Another aspect includes adding a respective first responder parity to each column set, wherein each first responder parity gives parity information for only the two or more columns in the first responder parity's respective column set.