Disclosed are devices, systems and methods for precoding and decoding polar codes using local feedback are described. One example method for improving an error correction capability of a decoder includes receiving a noisy codeword vector of length n, the codeword having been generated based on a concatenation of a convolutional encoding operation and a polar encoding operation and provided to a communication channel prior to reception by the decoder, performing a successive-cancellation decoding operation on the noisy codeword vector to generate a plurality of polar decoded symbols (n), generating a plurality of information symbols (k) by performing a convolutional decoding operation on the plurality of polar decoded symbols, wherein k/n is a rate of the concatenation of the convolutional encoding operation and the polar encoding operation, and performing a bidirectional communication between the successive-cancellation decoding operation and the convolutional decoding operation.

An LDPC code encoding method and a communication apparatus are described that provide increased redundant bits through retransmission in an IR-HARQ mechanism, so as to decrease a channel coding rate, and improve decoding performance of an LDPC code. A check matrix of the LDPC code is used as a basic matrix, and the basic matrix is extended to obtain a mother matrix compatible with a plurality of code rates. During LDPC encoding, a transmit device reads, from the mother matrix, a check matrix corresponding to a required code rate, and performs LDPC encoding on an information bit sequence based on the read check matrix. LDPC encoding is performed on the information bit sequence by using check matrices of different sizes, to obtain different quantities of redundant bits.

The present disclosure relates to a method, system, and non-transitory computer-readable storage medium for constructing a base matrix of a PBRL LDPC code, comprising: determining at least one candidate sub-matrix of a PBRL LDPC code based on a base matrix of a QR-QC-LDPC code; obtaining at least one count of cycles with at least one preset length for each of the at least one candidate sub-matrix; and determining a first sub-matrix of the base matrix of the PBRL LDPC code based on the at least one count of cycles.

A subspace pursuit apparatus for compressive sensing reconstruction includes: a first inner product unit configured to calculate a correlation between a residual vector and column vectors of a sensing matrix by calculating an inner product of them; a first sorting unit coupled to the first inner product unit and configured to select K column vector indices having highest correlations, where K is a sparsity level; a second inner product unit configured to calculate a matrix for calculating a pseudo-inverse matrix required for solving a least-squares from the sensing matrix to store in the Gram matrix buffer; a Cholesky inversion unit configured to perform a Cholesky decomposition of the matrix stored in the Gram matrix buffer and calculate an inverse of a decomposed matrix; and a sparse solution estimator configured to estimate the sparse solution from a matrix value of the matrix based on the inverse of the decomposed matrix.

An approach for correcting at least one byte error in a binary sequence is proposed, the binary sequence comprising a plurality of bytes and being a code word of an error code in the error-free case. The approach comprises the steps of: (i) determining at least one byte error position signal which specifies whether or not a byte of the binary sequence is erroneous, (ii) determining at least one byte error correction value, based on which an erroneous byte position identified by means of the byte error position signal is correctable, the at least one byte error correction value being determined by virtue of a first value and a second value being determined for each of at least two byte positions based on a coefficient of the locator polynomial, and (iii) correcting the at least one byte error based on the at least one byte error correction value.

A memory system includes a non-volatile memory and a controller. The controller is configured to, during a writing operation, generate a first error-detecting code from data that is input, perform a predetermined conversion on the data into first conversion data, generate a second error-detecting code from the first conversion data, and store the data, the first error-detecting code, and the second-error detecting code in the non-volatile memory. The controller is configured to during a read operation, read the data, the first error-detecting code, and the second error-detecting code from the non-volatile memory, perform a first error detection on the data using the first error-detecting code, perform the predetermined conversion on the data into second conversion data, perform a second error detection on the second conversion data using the second error-detecting code, and output the second conversion data based on results of the first and second error detections.

A low density parity check (LDPC) channel encoding method is used in a wireless communications system. A communication device encodes an input bit sequence by using an LDPC matrix, to obtain an encoded bit sequence for transmission. The LDPC matrix is obtained based on a lifting factor Z and a base matrix. The base matrix may be one of eight exemplary designs. The encoding method can be used in various communications systems including fifth generation (5G) telecommunication systems, and can support various encoding requirements for information bit sequences with different code lengths.

A data processing system includes a storage medium, and a controller including a data processing block, configured to receive data from a host, transmit the received data to the storage medium, read data from the storage medium in response to a read request from the host, and decode the read data by the data processing block according to multiple decoding modes. The data processing block includes a first decoder and a second decoder, and is configured to manage the first decoder and the second decoder to run the decoding for the read data, and activate a fast decoding having shorter latency than a normal decoding after a fast decoding condition is satisfied.

A memory system includes a semiconductor storage device and a memory controller including a storage circuit that stores correction value for read voltages in association with the word line, and a control circuit that reads data from the memory cells, performs a correction operation on the read data to determine a number of error bits therein, determines the correction value for each read voltage based on the number of error bits and a ratio of a lower tail fail bit count and an upper tail fail bit count, and stores the correction values for the read voltages in the storage circuit. The lower tail fail bit count represents the number of memory cells in a first state having threshold voltages of an adjacent state, and the upper tail fail bit count represents the number of memory cells in the adjacent state having threshold voltages of the first state.

A computer-implemented method includes fetching, by a controller, data using a plurality of memory channels of a memory system. The method further includes detecting, by the controller, that a first memory channel of the plurality of memory channels has not returned data. The method further includes marking, by the controller, the first memory channel from the plurality of memory channels as unavailable. The method further includes, in response to a fetch, reconstructing, by the controller, fetch data based on data received from all memory channels other than the first memory channel.