A data storage device includes a memory device and a controller coupled to the memory device. The controller is configured to create a dual parity matrix. The dual parity matrix includes a full parity form that includes a payload, a first parity portion, and a second parity portion and a reduced parity form that includes the payload and the first parity portion. The second parity portion is 0. The controller is further configured to create an incremental parity construction matrix. The incremental parity construction matrix includes two arrays. A first array includes a first payload portion, a first, first parity portion, and a first, second parity portion and a second array includes a second payload portion, a second, first parity portion, and a second, second parity portion. The incremental parity construction matrix is arranged in either a block triangular construction or a block diagonal construction.

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.

The present invention is directed to communication systems and methods. According to a specific embodiment, FEC data streams from multiple FEC data lanes are received. First stage interleaving and inner encoding are performed on the FEC data streams to generate inner encoded data streams. A second stage interleaving process is performed to interleave the inner encoded data streams. There are other embodiments as well.

A memory system according to an embodiment includes a nonvolatile memory and a memory controller. The nonvolatile memory includes a plurality of memory cells. The memory controller is configured to control the nonvolatile memory. In read operation for the memory cells, the memory controller is configured to: perform tracking including a plurality of reads in which a read voltage is shifted; determine a hard bit read voltage based on results of the tracking; calculate a soft bit read voltage based on the determined hard bit read voltage; perform soft bit read using the calculated soft bit read voltage; and perform a soft bit decoding process using a result of the soft bit read and a log-likelihood ratio table associated with the calculated soft bit read voltage.

A cyclic redundancy check, CRC, decoder circuit having a K-bit input bit sequence, s, comprising information bits and CRC bits; and at least one processor (P) configured to perform a CRC decode computation and configured to: use an inverse of a predefined CRC generator polynomial that encoded the K-bit input bit sequence, s, to produce a data set; compute a CRC syndrome from the data set; and determine whether the CRC syndrome contains any one-valued bits indicative of a CRC error. An LUT stores one or more rows of a CRC generator matrix (G) generated from the inverse of the predefined CRC generator polynomial. A set of mod(−K,P) zero-valued filler bits are appended to an end of the K-bit input bit sequence, wherein an order of the rows in the CRC generator matrix (G) is reversed and aligned with the input bits of the input stream.

A syndrome calculation circuit includes a matrix product calculation circuit. The matrix product calculation circuit is configured to generate syndrome bits in a composite field by calculating a matrix product of input data bits and a first arithmetic matrix. The first arithmetic matrix is a matrix product of a basis conversion matrix for converting a data string from a Galois field to the composite field and a second arithmetic matrix, which is at least a part of a parity check matrix.

A memory device and a system that implements a single symbol correction, double symbol detection (SSC-DSD+) error correction scheme are provided. The scheme is implemented by calculating four syndrome symbols in accordance with a Reed-Solomon (RS) codeword; determining three location bytes in accordance with three corresponding pairs of syndrome symbols in the four syndrome symbols; and generating an output based on a comparison of the three location bytes. The output may include: corrected data responsive to determining that the three location bytes match; an indication of a detected-and-corrected error (DCE) responsive to determining that two of the three location bytes match; or an indication of a detected-yet-uncorrected error (DUE) responsive to determining that none of the three location bytes match. A variant of the SSC-DSD+ decoder may be implemented using a carry-free subtraction operation to perform sanity checking.

Methods and systems described herein are directed to encoding information bits for transmission. The methods can include receiving a set of information bits (900) and determining a set of parity check bits (910). The set of information bits is concatenated with the set of parity check bits (920), and the information bits are polar encoded into a set of information bits and frozen bits (930). The encoded set of information bits is transmitted to a wireless receiver (940). In particular embodiments, each parity check bit in the set of parity check bits is the binary sum of the values of all bits in front of it. Other embodiments include generating a set of parity check bits based on a systematic block code on the least reliable bits of the set of information bits. The methods and systems described herein may be applied to 3GPP 5G mobile communication systems.

Methods, systems, and apparatus, including computer programs encoded on computer-storage media, for improving communication throughput despite periodic blockages. In some implementations, a method includes receiving, by a receiver and from a transmitter, code blocks transmitted according to a first set of communication parameters that includes one or more first interleaver parameters used to interleave information in the code blocks prior to transmission. Corrupted portions of at least some of the received code blocks are identified. A blockage duration and a blockage interval of a blockage of communication channel between the transmitter and the receiver are determined based on the corrupted portions of the received code blocks. A second set of communication parameters that includes one or more second interleaver parameters are determined based on the blockage duration and blockage interval. The second set of communication parameters are communicated to the transmitter for subsequent transmissions by the transmitter to the receiver.

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.