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.

Provided herein may be an error correction decoder, an error correction circuit having the error correction decoder, and a method of operating the error correction decoder. The error correction decoder may include a calculator configured to output an error correction message by performing an iterative decoding operation on a first codeword, a syndrome generator configured to generate a syndrome by calculating the error correction message and a parity check matrix and to output a number of iterations representing the number of times the iterative decoding operation has been performed, and an unsatisfied check node (UCN) value representing the number of unsatisfied check nodes in the syndrome, and a speed selector configured to output a speed code for controlling a speed of the iterative decoding operation depending on the number of iterations and the UCN value.

Example systems, read channels, and methods provide bit value detection from an encoded data signal using a neural network soft information detector. The neural network detector determines a set of probabilities for possible states of a data symbol from the encoded data signal. A soft output detector uses the set of probabilities for possible states of the data symbol to determine a set of bit probabilities that are iteratively exchanged as extrinsic information with an iterative decoder for making decoding decisions. The iterative decoder outputs decoded bit values for a data unit that includes the data symbol.

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.

A method for handling a read error on a block of a memory device is disclosed. In response to a read failure indicating that at least one error handling mechanism has handled the read error on the block and fails to read data stored in the block, a memory test is trigged to be performed on the block. The memory test is configured to determine whether the block malfunctions.

Examples described herein utilize multi-layer neural networks, such as multi-layer recurrent neural networks to estimate message probability compute data based on encoded data (e.g., data encoded using one or more encoding techniques). The neural networks and/or recurrent neural networks may have nonlinear mapping and distributed processing capabilities which may be advantageous in many systems employing a neural network or recurrent neural network to estimate message probability compute data for a message probability compute (MPC) decoder. In this manner, neural networks or recurrent neural networks described herein may be used to implement aspects of error correction coding (ECC) decoders, e.g., an MPC decoder that iteratively decodes encoded data.

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.

Methods and systems for decoding raw data may include determining a sequence of a plurality of read-level voltages based on previous decoding data and executing a multi-stage decoding operation to decode raw data read from the plurality of memory cells using the determined sequence of the plurality of read-level voltages. Decoded data is returned from the multi-stage decoding operation upon completion of the multi-stage decoding operation and the previous decoding data is updated based on results of the multi-stage decoding operation.

A forward error correction (FEC) decoder is configured to find an alignment of a code block in a data stream by attempting to fully or partially decode one or more data windows of a predetermined size in the data stream. The predetermined size is a size of each codeword. The FEC decoder selects a first data window of the predetermined size, attempts to decode the first data window based on a particular error control coding method, and determines whether a valid codeword can be identified by attempting to decode the first data window. In response to determining that a valid codeword can be identified, the FEC decoder determines that an alignment of the codeword with the first data window is found. Otherwise, the FEC decoder selects a second data window of the predetermined size and attempts to decode the second data window.

A method of responding to a read request from a host includes: obtaining read data from a memory device, performing first iteration ECC decoding on the read data to generate a plurality of pieces of decoded data, selecting one of the plurality of pieces of decoded data as intermediate data as intermediate data, generating preprocessed data based on the read data and the intermediate data and performing second iteration ECC decoding on the preprocessed data when the first iteration ECC decoding fails, and outputting the intermediate data to the host when the first iteration ECC decoding succeeds.