Systems and methods for improving the error floor performance in decoding generalized product codes (GPC) are described. The systems and methods can implement a two stage process to decode a GPC block code and break a stall error pattern for the decoding the block code. In the first stage, erroneuous bits in a codeword can be flagged. In the second stage, some of these bits and related bits in a codeword can be toggled to generate one or more test patterns. The test patterns can be decoded and one of them can be selected using a particular selection criteria to ultimately break the stall error pattern and improve the error floor performance.

According to one embodiment, a memory system includes a non-volatile memory, a memory interface that reads data recorded in the non-volatile memory as a received value, a converting unit that converts the received value to first likelihood information by using a first conversion table, a decoder that decodes the first likelihood information, a control unit that outputs an estimated value with respect to the received value, which is a decoding result obtained by the decoding, when decoding by the decoder has succeeded, and a generating unit that generates a second conversion table based on a decoding result obtained by the decoding, when decoding of the first likelihood information by the decoder has failed. When the generating unit generates the second conversion table, the converting unit converts the received value to the second likelihood information by using the second conversion table, and the decoder decodes the second likelihood information.

As system is provided for performing a method of receiving a superposition state defined by a sum of a plurality of addends, wherein each addend of the plurality of addends is a product between a corresponding coefficient of a plurality of coefficients and a corresponding state of a plurality of states encoded with block unary encoding. The system may identify at least one error state, of the plurality of states, having a string value that is not a block unary code string of a set of block unary code strings. The system may compute an updated superposition state based on the plurality of states without the error state.

An error correcting code (ECC) decoder for a non-volatile memory device is configured to decode data stored by the non-volatile memory device using a parity check matrix with columns of different column weights. The ECC decoder is further configured to artificially slow processing of one or more of the columns of the parity check matrix in response to column weights for the one or more columns satisfying a threshold.

Compact timestamps and related methods, systems and devices are described. An encoder is configured to generate compact timestamps of the disclosure by sampling states of linear feedback shift registers (LFSRs). A decoder may be configured to determine timing information responsive to the compact timestamps.

A data storage device includes a nonvolatile memory device configured to read and output a plurality of data chunks; and a data processing block configured to perform decoding on the data chunks, the data processing block comprising a sequencer configured to generate a decoding information on the data chunks; and a core circuit configured to perform normal decoding on a first data chunk among the data chunks based on the decoding information, and perform fast decoding on a second data chunk among the data chunks depending on whether a result of the normal decoding satisfies a fast decoding condition, wherein the fast decoding requires a shorter execution time than the normal decoding.

Systems and methods are provided for decoding data read from non-volatile storage devices. A method may comprise receiving a chunk of data read from a physical location of a non-volatile storage device and searching a memory for soft information associated with the physical location using a unique identifier associated with the physical location. The soft information may be generated from one or more previous decoding processes on previous data from the physical location. The method may further comprise retrieving the soft information identified by the unique identifier associated with the physical location from the memory, decoding the chunk of data with the soft information indicating reliability of bits in the chunk of data and updating the soft information with decoding information generated during the decoding.

An LDPC decoding method of a received signal including a plurality of received symbols is provided. A decoding apparatus selects a perturbation space in which perturbation is to be performed based on a code length of the received signal and a maximum number of perturbation rounds indicating a number of perturbation rounds that can be performed, and performs a perturbation round. The decoding apparatus performs perturbation on a corresponding received symbol among the plurality of received symbols in each perturbation round, and decodes the received signal on which the perturbation has been performed. The decoding apparatus determines that decoding is successful when there is a perturbation round in which a decoding result of the received signal satisfies a predetermined condition.

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.

Devices and methods described herein decode a sequence of coded symbols by guessing noise. In various embodiments, noise sequences are ordered, either during system initialization or on a periodic basis. Then, determining a codeword includes iteratively guessing a new noise sequence, removing its effect from received data symbols (e.g. by subtracting or using some other method of operational inversion), and checking whether the resulting data are a codeword using a codebook membership function. This process is deterministic, has bounded complexity, asymptotically achieves channel capacity as in convolutional codes, but has the decoding speed of a block code. In some embodiments, the decoder tests a bounded number of noise sequences, abandoning the search and declaring an erasure after these sequences are exhausted. Abandonment decoding nevertheless approximates maximum likelihood decoding within a tolerable bound and achieves channel capacity when the abandonment threshold is chosen appropriately.