There is provided a decoding circuit including; a first decoding unit that decodes a first signal from a multiplexed signal in which the first signal and a second signal are multiplexed in an LDM (Layered Division Multiplexing) system; and a second decoding unit that decodes the second signal from the multiplexed signal using the decoding result of the decoded first signal, wherein the second signal is selectively decoded based on noise information related to a reception state of the multiplexed signal.

Examples described herein utilize multi-layer neural networks to decode encoded data (e.g., data encoded using one or more encoding techniques). The neural networks have nonlinear mapping and distributed processing capabilities which are advantageous in many systems employing the neural network decoders. In this manner, neural networks described herein are used to implement error code correction (ECC) decoders.

A storage device includes: a memory; and a processor configured to, at the time of writing data into the memory, generate a first check code common to a plurality of types of error correction codes from the data on the basis of a correlation relationship between the plurality of types of error correction codes, add the first check code to the data and write the data into the memory, convert the first check code into a second check code based on any one of the plurality of types of error correction codes at the time of reading the data from the memory, and perform error correction by using the second check code.

A transmitter is provided. The transmitter includes: a Low Density Parity Check (LDPC) encoder configured to encode input bits to generate parity bits; a parity permutator configured to perform parity permutation by interleaving the parity bits and group-wise interleaving a plurality of bit groups including the interleaved parity bits; and a puncturer configured to puncture some of the parity bits in the group-wise interleaved bit groups, wherein the parity permutator group-wise interleaves the bit groups such that some of the bit groups are positioned at predetermined positions, respectively, and a remainder of the bit groups are positioned without an order within the group-wise interleaved bit groups.

A transmitter is provided. The transmitter includes: an outer encoder configured to encode input bits to generate outer-encoded bits including the input bits and parity bits; a zero padder configured to generate a plurality of bit groups each of which is formed of a same number of bits, maps the outer-encoded bits to some of the bits in the bit groups, and pads zero bits to remaining bits in the bit groups, based on a predetermined shortening pattern, thereby to constitute Low Density Parity Check (LDPC) information bits; and an LDPC encoder configured to encode the LDPC information bits, wherein the remaining bits in which zero bits are padded include some of the bit groups which are not sequentially disposed in the LDPC information bits.

In general, according to an embodiment, a memory system includes a memory device including a memory cell; and a controller. The controller is configured to: receive first data from the memory cell in a first data reading; receive second data from the memory cell in a second data reading that is different from the first data reading; convert a first value that is based on the first data and the second data, to a second value in accordance with a first relationship; and convert the first value to a third value in accordance with a second relationship that is different from the first relationship.

This application discloses example decoding methods, example decoder, and example decoding apparatuses. One example decodine method includes performing soft decision decoding on a first sub-codeword in a plurality of sub-codewords to obtain a hard decision result. It is determined whether to skip a decoding iteration. In response to determining not to skip the decoding iteration, a first turn-off identifier corresponding to the first sub-codeword is set to a first value based on the hard decision result. The first turn-off identifier indicates whether to perform soft decision decoding on the first sub-codeword in a next decoding iteration. The soft decision decoding is not performed on the first sub-codeword in the next decoding iteration when a value indicated by the first turn-off identifier is the first value. The hard decision result is stored.

An example methods for interleaved BCH codes can include encoding a plurality of portions of data using a first generator polynomial to obtain a plurality of respective BCH codewords. The method can include encoding an additional BCH codeword based at least in part on a second plurality of portions of data and the plurality of BCH codewords using a second generator polynomial. The method can include outputting the plurality of respective BCH codewords and the additional BCH codeword.

Methods, systems and devices for forward error correction in orthogonal time frequency space (OTFS) communication systems using non-binary low-density parity-check (NB-LDPC) codes are described. One exemplary method for forward error correction includes receiving data, encoding the data via a non-binary low density parity check (NB-LDPC) code, wherein the NB-LDPC code is characterized by a matrix with binary and non-binary entries, modulating the encoded data to generate a signal, and transmitting the signal. Another exemplary method for forward error correction includes receiving a signal, demodulating the received signal to produce data, decoding the data via a NB-LDPC code, wherein the NB-LDPC code is characterized by a matrix with binary and non-binary entries, and providing the decoded data to a data sink.

A memory system includes an encoder and a decoder. The encoder is configured to generate multi-dimensionally-coded data to be written into the non-volatile memory. Data bits of the multi-dimensionally-coded data are grouped into first and second dimensional codes with respect to first and second dimensions, respectively. The decoder is configured to, with respect to each of the first and second dimensional codes included in read multi-dimensionally-coded data, generate a syndrome value of the dimensional code, generate low-reliability location information, generate a soft-input value based on the syndrome value and the low-reliability location information, decode the dimensional code through correction of the dimensional code using the soft-input value, and store modification information indicating a bit of the dimensional code corrected through the correction and reliability information indicating reliability of the correction. The decoder generates the soft-input value also based on the modification information and the reliability information in the memory.