A method of correcting data stored in a memory device includes: applying an iterative decoder to the data; determining a total number of rows in first data the decoder attempted to correct; estimating first visible error rows among the total number that continue to have an error after the attempt; estimating residual error rows among the total number that no longer have an error after the attempt; determining second visible error rows in second data of the decoder that continue to have an error by permuting indices of the residual error rows according to a permutation; and correcting the first data using the first visible error rows.

Embodiments of the present disclosure provide a scheme for decoding over a small subgraph which highly likely includes some errors. A controller is configured to: control the first decoder to decode the data, read from the memory device, using a parity check matrix for the error correction code; extract one or more subgraphs from the entire bipartite graph of the parity check matrix, which is defined by a plurality of variable nodes and a plurality of check nodes when a particular condition satisfied; and control the second decoder to decode the decoding result of the first decoder using a submatrix of the parity check matrix corresponding to the extracted subgraphs.

A method of correcting data stored in a memory device includes: applying an iterative decoder to the data; determining a total number of rows in first data the decoder attempted to correct; estimating first visible error rows among the total number that continue to have an error after the attempt; estimating residual error rows among the total number that no longer have an error after the attempt; determining second visible error rows in second data of the decoder that continue to have an error by permuting indices of the residual error rows according to a permutation; and correcting the first data using the first visible error rows.

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 memory device having a Low-Density Parity-Check (LDPC) decoder that is energy efficient and has a low error floor. The decoder is configured to determine syndromes of bits in a codeword, select bits in the codeword based at least in part on the syndromes according to a first mode, and flip the selected bits in the codeword. The decoder can repeat the bit selection and flipping operations to iteratively improve the codeword and reduce parity violations. Further, the decoder can detect a pattern in parity violations of the codeword in its iterative bit flipping operations. In response, the decoder can change from the first mode to a second mode in bit selection for flipping. For example, the decoder can transmit from a dynamic syndrome mode to a static syndrome mode in response to the pattern of repeating a cycle of bit flipping iterations.

A memory device having a Low-Density Parity-Check (LDPC) decoder that is energy efficient and has a low error floor. The decoder is configured to determine syndromes of bits in a codeword, select bits in the codeword based at least in part on the syndromes according to a first mode, and flip the selected bits in the codeword. The decoder can repeat the bit selection and flipping operations to iteratively improve the codeword and reduce parity violations. Further, the decoder can detect a pattern in parity violations of the codeword in its iterative bit flipping operations. In response, the decoder can change from the first mode to a second mode in bit selection for flipping. For example, the decoder can transmit from a dynamic syndrome mode to a static syndrome mode in response to the pattern of repeating a cycle of bit flipping iterations.

A memory device having a Low-Density Parity-Check (LDPC) decoder that is energy efficient and has a low error floor. The decoder is configured to determine syndromes of bits in a codeword, select bits in the codeword based at least in part on the syndromes according to a first mode, and flip the selected bits in the codeword. The decoder can repeat the bit selection and flipping operations to iteratively improve the codeword and reduce parity violations. Further, the decoder can detect a pattern in parity violations of the codeword in its iterative bit flipping operations. In response, the decoder can change from the first mode to a second mode in bit selection for flipping. For example, the decoder can transmit from a dynamic syndrome mode to a static syndrome mode in response to the pattern of repeating a cycle of bit flipping iterations.

Disclosed are devices, systems and methods for error correction decoding using an iterative decoding scheme. An error correction circuit includes a node processor to perform a plurality of iterations for updating values of one or more variable nodes and one or more check nodes using initial values assigned to the one or more variable nodes, respectively, a trapping set detector to detect a trapping set in at least one of the plurality of iterations by applying a predetermined trapping set determination policy, and a post processor to reduce at least one of the initial values or invert at least one of values of the variable nodes corresponding to an iteration in which the trapping set is detected, upon detection of the trapping set.

An LDPC decoding method of a received signal including a plurality of received symbols is provided. A decoding apparatus selects a perturbation space in which perturbation is to be performed based on a code length of the received signal and a maximum number of perturbation rounds indicating a number of perturbation rounds that can be performed, and performs a perturbation round. The decoding apparatus performs perturbation on a corresponding received symbol among the plurality of received symbols in each perturbation round, and decodes the received signal on which the perturbation has been performed. The decoding apparatus determines that decoding is successful when there is a perturbation round in which a decoding result of the received signal satisfies a predetermined condition.

A flash memory controller used to access a flash memory includes a read-only memory, a processor, and an error correction code unit. The read-only memory is used to store a code. The processor executes the code to control access to the flash memory. The error correction code unit includes a control module and a decoder. The control module respectively calculates a first correlation between innate bad-column information which records the location of innate bad columns that become damaged after the read-only memory being manufactured and a plurality of trapping sets of a plurality of preset LDPC (low-density parity check) codes and uses the preset LDPC code which has the lowest first correlation as a selected LDPC code. The decoder decodes read information obtained from the flash memory according to the selected LDPC code.