A memory system includes a non-volatile memory and a memory controller. During a read operation to read data stored in the non-volatile memory as an N-dimensional error correction code, where N is two or more, the memory controller performs an error correction process on the N-dimensional error correction code iteratively, the error correction process including a first decoding process on a first decoding input to produce a first decoding output and a second decoding process on a second decoding input to produce a second decoding output. During the error correction process, upon determining that errors remaining in the second decoding output after a most recent iteration would not be correctable, the memory controller performs a next iteration using a first decoding input for the next iteration, which is a modified form of the second decoding output of the most recent iteration.

A hard-decision (HD) forward error correcting (FEC) coded signal is decoded by a soft-aided decoder (112) to produce decoded bits (118) using marked reliable bits of the HD-FEC coded signal and marked unreliable bits of the HD-FEC coded signal (soft-aided bit marking) that are computed by calculation (114) and marking blocks (116) based on an absolute value of log-likelihood ratios (LLRs) of the HD-FEC coded signal. The hard-decision (HD) forward error correcting (FEC) coded signal may be, for example, a staircase code (SCC) coded signal or a product code (PC) coded signal.

A memory system includes a non-volatile memory and a controller. The controller is configured to perform iterative correction on a plurality of frames of data read from the non-volatile memory. The iterative correction includes performing a first error correction on each of the frames including a first frame having errors not correctable by the first error correction, generating a syndrome on a set of second frames that include the first frame, performing a second error correction on the second frames using the syndrome, and performing a third error correction on the first frame. Each of the frames includes user data and first parity data used in the first error correction, the first parity data of the first frame also being used in the third error correction.

Various implementations described herein relate to systems and methods for decoding data stored in a non-volatile storage device, including determining features for each of a plurality of component codes corresponding to the data by decoding each of the plurality of component codes, determining an extrinsic value output for each of the component codes based on the features, and after the extrinsic value output for each of the component codes is determined, decoding each of the plurality of component codes based on the extrinsic value outputs of all other component codes of the component codes. Each of the component codes depends on all other component codes.

A memory controller for use in a data storage device is provided. The memory controller includes a variable-node circuit and a check-node circuit. The check-node circuit is configured to obtain a codeword difference from the variable-node circuit, and calculate a syndrome according to the codeword difference. During each LDPC (low-density parity check) decoding iterative operation, the variable-node circuit executes the following steps: determining syndrome weight according to a channel value and the syndrome from the check-node circuit; obtaining a previous codeword generated by a previous LDPC decoding iterative operation; determining a flipping strategy of a bit-flipping algorithm for each codeword bit in the previous codeword according to the syndrome weight and a predetermined threshold, and flipping one or more codeword bits in the previous codeword according to the flipping strategy to generate an updated codeword; and subtracting the previous codeword from the updated codeword to generate the codeword difference.

A method for decoding a signal encoded with polar codes by a decoding system is provided. The method comprises receiving, from a transmission system, a signal in which a plurality of cyclic redundancy checks (CRCs) are encoded by the polar codes, the plurality of CRCs being inserted into positions determined based on a plurality of information bits, a number of the plurality of information bits and a total code length, and decoding a code section including bits ranging from a first bit of the signal to a position where a last bit of a first CRC is inserted. The method further comprises re-performing successive cancellation flip decoding for the decoded code section, or determining whether to decode a next code section adjacent to the decoded code section, based on whether a CRC is detected in the decoded code section.

A decoding circuit includes a Bose-Chaudhuri-Hocquenghem (BCH) decoder. The BCH decoder includes a Syndrome stage for generating syndromes based on a BCH encoded word, a Berlekamp-Massey (BM) stage performing a Berlekamp-Massey algorithm on the syndromes to generate Error Location Polynomial (ELP) coefficients, a Chien stage that performs a Chien search on the ELP coefficients using a Fast Fourier Transform (FFT) to generate error bits and iteration information, and a Frame Fixer stage configured to reorder the error bits to be sequential based on the iteration information. The BCH decoder decodes the BCH encoded word using the reordered error bits.

A memory controller for use in a data storage device is provided. The memory controller includes a variable-node circuit and a check-node circuit. The check-node circuit is configured to obtain a codeword difference from the variable-node circuit, and calculate a syndrome according to the codeword difference. During each LDPC (low-density parity check) decoding iterative operation, the variable-node circuit executes the following steps: determining syndrome weight according to a channel value and the syndrome from the check-node circuit; obtaining a previous codeword generated by a previous LDPC decoding iterative operation; determining a flipping strategy of a bit-flipping algorithm for each codeword bit in the previous codeword according to the syndrome weight and a predetermined threshold, and flipping one or more codeword bits in the previous codeword according to the flipping strategy to generate an updated codeword; and subtracting the previous codeword from the updated codeword to generate the codeword difference.

A set of bits of a segment of a memory device that is associated with an unsuccessful first decoding operation can be identified. A discrepancy value for at least one bit of the set of bits can be calculated. It can be determined whether the discrepancy value calculated for the at least one bit of the set of bits corresponds to a correction capability of the failed decoding operation. In response to determining that the discrepancy value calculated for the at least one bit corresponds to the correction capability of the failed decoding operation, the at least one bit of the set of bits can be corrected by switching a value of the at least one bit.

A data transmitting method using an LDPC code as an error correction code is provided. The method includes providing a parity check matrix of LDPC code, wherein the size of the parity check matrix is (m1+m2)×(n1+n2); in a sending side, encoding an input data of K bits with a encoder to generate a first block code of (n1+n2) bits, according to the parity check matrix; through a transmitting channel, sending n1 bits of the first block code from the sending side to a receiving side, wherein n2 bits of the first block code are not transmitted; and receiving the n1 bits of the first block code in the receiving side, and using the parity check matrix to perform a decoding algorithm to the received first block code to iterative decodes a second block code of (n1+n2) bits with a decoder. Furthermore, a data decoding method thereof is also provided.