A bit interleaving method applying a bit permutation process to a QC LDPC codeword made up of N cyclic blocks of Q bits each, dividing the processed codeword into constellation words of M bits each, and applying an intra-cyclic-block permutation process to the cyclic blocks, where the codeword is divided into F×N/M folding sections of M/F cyclic blocks each and the constellation words are each associated with one of the folding sections, and the bit permutation process is applied such that the constellation words are each made up of F bits from each of M/F different cyclic blocks in the associated section, after the permutation process.

A loss correction encoding device having an improved capability of loss correction using LDPC-CC includes a rearranging unit that rearranges information data contained in n information packets according to the constraint length Kmax and the encoding rate (q−1)/q of a check polynomial of the loss correction code used in a loss correction encoding unit. Specifically, the rearranging unit rearranges the information data in such a way that continuous Kmax×(q−1) pieces of information data after rearrangement are contained in different information packets. The rearranging unit distributes the information data to information blocks from n information packets, where n satisfies the formula Kmax×(q−1)≤n.

A memory system includes a memory device and a controller. The memory device is configured to supply a read voltage into a plurality of non-volatile memory cells and transfer values obtained from the plural non-volatile memory cells. The controller is coupled to the memory device via at least one channel. The controller adjusts a level of the read voltage based on a cell difference probability (CDP) calculated from the values when a read operation to the plurality of non-volatile memory cells fails.

A method and a device of selecting a base graph of a low-density parity-check code are provided. The method includes: acquiring a data information length and a channel coding rate of to-be-encoded data; determining a target base graph selection strategy according to the data information length and an information length range of a base graph; determining a target base graph for the to-be-encoded data according to the target base graph selection strategy and the channel coding rate.

A decoder that is a decoding apparatus includes an error-correction decoder that executes error correction decoding processing of iteratively performing decoding processing with a window size and the number of decoding iterations indicated by decoding parameters, on received data converted into a spatially coupled low-density parity-check code, and a decoding parameter control unit that updates the decoding parameters on the basis of a decoding result obtained by the iteratively executed decoding processing.

Disclosed are systems, methods, and software for generating spatially-coupled low-density parity-check (SC-LDPC) codes. A method for generating SC-LDPC codes includes generating one or more quasi-cyclic low-density parity-check (QC-LDPC) codes, and also includes assigning at least one of the generated one or more QC-LDPC codes as one or more template codes. The method further includes copying at least a portion of the one or more template codes to introduce irregularity. The method also includes shifting one or more template codes on a sub-block basis to generate at least one SC-LDPC code. As compared to known LDPC code generation modalities, the disclosed invention provides a simplified technique for implementation in streamlined hardware which has more general applicability across both present, and anticipated, communication systems, including those adapted for use with optical communications, wireless communications, and 5G as well as future 6G.

A loss correction encoding device having an improved capability of loss correction using LDPC-CC includes a rearranging unit that rearranges information data contained in n information packets according to the constraint length Kmax and the encoding rate (q−1)/q of a check polynomial of the loss correction code used in a loss correction encoding unit. Specifically, the rearranging unit rearranges the information data in such a way that continuous Kmax×(q−1) pieces of information data after rearrangement are contained in different information packets. The rearranging unit distributes the information data to information blocks from n information packets, where n satisfies the formula Kmax×(q−1)≤n.

A decoding method includes inputting coded data, and decoding the coded data to obtain decoded data. The coded data are generated by using an encoding process at an encoding apparatus, and the encoding process includes: (i) repeatedly-selecting and collecting first packets included in the decoded data to generate at least one second packet; (ii) dividing at least one third packet included in the decoded data into fourth packets; and (iii) allocating fifth packets included in the decoded data to respective sixth packets without collecting the first packets or dividing the at least one third packet, and performing an error correcting encoding on the at least one second packet, the fourth packets, and the sixth packets in accordance with a coding rate selected from a plurality of coding rates to generate parity data.

A bit interleaving method applying a bit permutation process to a QC LDPC codeword made up of N cyclic blocks of Q bits each, dividing the processed codeword into constellation words of M bits each, and applying an intra-cyclic-block permutation process to the cyclic blocks, where the codeword is divided into F×N/M folding sections of M/F cyclic blocks each and the constellation words are each associated with one of the folding sections, and the bit permutation process is applied such that the constellation words are each made up of F bits from each of M/F different cyclic blocks in the associated section, after the permutation process.

Systems and methods herein provide for error correction via Low Density Parity Check (LDPC) coding. In one embodiment, a system includes a data buffer operable to receive a block of Low Density Parity Check (LDPC) encoded data. The system also includes a processor operable to reduce a belief propagation algorithm used to encode the LDPC encoded data into a quadratic polynomial, to embed the quadratic polynomial onto a plurality of quantum bits (qubits), and to decode the block of LDPC encoded data via the qubits.