An encoding method includes: receiving, by an encoder, an information for encoding; generating, by the encoder, a first portion codeword according to a first encoding rule and the information for encoding, wherein the first encoding rule is an encoding rule configured to generate LDPC code; generating, by the encoder, a second portion codeword according to a second encoding rule different from the first encoding rule and a double check region of the first portion codeword; and concatenating, by the encoder, the first portion codeword and the second portion codeword to generate a codeword. A plurality of trapping sets corresponding to the first encoding rule include at least one error bit within the double check region.

A semiconductor memory system including: a semiconductor memory device suitable for storing a codeword; and an LDPC decoder suitable for decoding the codeword to generate decoded data, wherein the LDPC decoder includes: a message passing decoding component suitable for performing a first decoding operation of decoding the codeword, and calculating the minimum value among numbers of UCNs; and an error path detection component suitable for detecting error path candidates using a tree in which each of UCNs corresponding to the minimum value is set to a root node, sorting the detected error path candidates in ascending order of maximum LLRs, resetting symbol values and LLRs of variable nodes in the error path candidates, and providing the message passing decoding unit with information on the reset symbol values and LLRs.

The present invention discloses an encoder, a decoder, an encoding method and a decoding method based on Low-Density Parity-Check (LDPC) code. The encoding method comprises: receiving, by an encoder, an information for encoding; generating, by the encoder, a first portion codeword according to a first encoding rule and the information for encoding, wherein the first encoding rule is an encoding rule configured to generate LDPC code; generating, by the encoder, a second portion codeword according to a second encoding rule different from the first encoding rule and a double check region of the first portion codeword; and concatenating, by the encoder, the first portion codeword and the second portion codeword to generate a codeword. A plurality of trapping sets corresponding to the first encoding rule include at least one error bit within the double check region.

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 FN/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.

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.

A method for generating an LDPC (low-density parity check) code with a required error floor, comprising: using a parity generation circuit to generate an LDPC code; using a detection circuit to detect the LDPC code according to a plurality of trapping set cores in a database and to generate at least one piece of trapping-set-core information; using a verification circuit to perform an important sampling simulation according to the LDPC code and each trapping-set-core information separately to obtain an estimated error floor for each trapping-set-core information; using the verification circuit to separately compare each of the estimated error floors with an expected error floor; and when all of the estimated error floors are lower than or equal to the expected error floor, using the verification circuit to output the LDPC code.

Described herein is an error correction circuit that includes a syndrome check history manager configured to maintain a history of syndrome checks corresponding to one or more iterations of the iterative decoding scheme. The error correction circuit also includes a trapping set detector configured to compare a trapping set determination policy with the history of syndrome checks to determine whether the history of syndrome checks meets criteria of the trapping set determination policy, while error correction decoding is performed, and determine that a trapping set exists when the history of syndrome checks satisfies the trapping set determination policy. The trapping set determination policy is related to at least one of a change in a syndrome vector, a number of UCNs, and a change in the number of UCNs.

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 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.

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 FN/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.

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.