Abstract: A method for Bose-Chaudhuri-Hocquenghem (BCH) soft error decoding includes receiving a codeword x, wherein the received codeword x has ?=t+r errors for some r?1; computing a minimal monotone basis {?i(x)}1?i?r+1?F[x] of an affine space V={?(x)?F[x]:?(x)·S(x)=??(x) (mod x2t), ?(0)=1, deg(?(x)?t+r}, wherein ?(x) is an error locator polynomial and S(x) is a syndrome; computing a matrix A?(?j(?i))i?[w],j?[r+1], wherein W={?1, . . . , ?w} is a set of weak bits in x; constructing a submatrix of r+1 rows from sub matrices of r+1 rows of the subsets of A such that the last column is a linear combination of the other columns; forming a candidate error locating polynomial using coefficients of the minimal monotone basis that result from the constructed submatrix; performing a fast Chien search to verify the candidate error locating polynomial; and flipping channel hard decision at error locations found in the candidate error locating polynomial.

Abstract: Systems and methods of the present disclosure may be used to improve equalization module architectures for NAND cell read information. For example, embodiments of the present disclosure may provide for de-noising of NAND cell read information using a Multiple Shallow Threshold-Expert Machine Learning Models (MTM) equalizer. An MTM equalizer may include multiple shallow machine learning models, where each machine learning model is trained to specifically solve a classification task (e.g., a binary classification task) corresponding to a weak decision range between two possible read information values for a given NAND cell read operation. Accordingly, during inference, each read sample with a read value within a weak decision range is passed through a corresponding shallow machine learning model (e.g., a corresponding threshold expert) that is associated with (e.g., trained for) the particular weak decision range.

Abstract: A method for Bose-Chaudhuri-Hocquenghem (BCH) soft error decoding includes receiving a codeword x, wherein the received codeword x has ?=t+r errors for some r?1; computing a minimal monotone basis {?i(x)}1?i?r+1?F[x] of an affine space V={?(x)?F[x]: ?(x)·S(x)=??(x) (mod x2t), ?(0)=1, deg(?(x)?t+r}, wherein ?(x) is an error locator polynomial and S(x) is a syndrome; computing a matrix A?(?j?i))i?[W],j?[r+1], wherein W={?i, . . . , ?W} is a set of weak bits in x; constructing a submatrix of r+1 rows from sub matrices of r+1 rows of the subsets of A such that the last column is a linear combination of the other columns; forming a candidate error locating polynomial using coefficients of the minimal monotone basis that result from the constructed submatrix; performing a fast Chien search to verify the candidate error locating polynomial; and flipping channel hard decision at error locations found in the candidate error locating polynomial.

Abstract: A device for decoding a generalized concatenated code (GCC) codeword includes: a buffer; and at least one processor configured to: obtain the GCC codeword, calculate a plurality of inner syndromes based on a plurality of frames; calculate a plurality of sets of delta syndromes based on the frames; determine a plurality of outer syndromes based on the sets of delta syndromes; store the inner syndromes and the outer syndromes in a buffer; perform inner decoding on the frames based on the inner syndromes stored in the buffer; update at least one outer syndrome stored in the buffer based on a result of the inner decoding; perform outer decoding on the frames based on the updated at least one outer syndrome; and obtain decoded information bits corresponding to the GCC codeword based on a result of the inner decoding and the result of the outer decoding.

Abstract: A method, apparatus, non-transitory computer readable medium, and system for selecting program voltages for a memory device are described. Embodiments of the method, apparatus, non-transitory computer readable medium, and system may map a set of information bits to voltage levels of one or more memory cells based on a plurality of embedding parameters, program the set of information bits into the one or more memory cells based on the mapping, detect the voltage levels of the one or more memory cells to generate one or more detected voltage levels, and identify a set of predicted information bits based on the one or more detected voltage levels using a neural network comprising a plurality of network parameters, wherein the network parameters are trained together with the embedding parameters.

Abstract: A memory system includes a memory device and a memory controller. The memory device includes a plurality of memory cells. The memory controller includes an error correction code (ECC) circuit. The ECC circuit is configured to determine data rows of first write data that are not all zeros and store the determined data rows in buffer rows of a buffer along with corresponding row indexes. The memory controller is configured to write second data based on the buffer to the memory device.

Abstract: Systems and methods of the present disclosure may be used to improve equalization module architectures for NAND cell read information. For example, embodiments of the present disclosure may provide for de-noising of NAND cell read information using a Multiple Shallow Threshold-Expert Machine Learning Models (MTM) equalizer. An MTM equalizer may include multiple shallow machine learning models, where each machine learning model is trained to specifically solve a classification task (e.g., a binary classification task) corresponding to a weak decision range between two possible read information values for a given NAND cell read operation. Accordingly, during inference, each read sample with a read value within a weak decision range is passed through a corresponding shallow machine learning model (e.g., a corresponding threshold expert) that is associated with (e.g., trained for) the particular weak decision range.

Abstract: A method, apparatus, non-transitory computer readable medium, and system for selecting program voltages for a memory device are described. Embodiments of the method, apparatus, non-transitory computer readable medium, and system may map a set of information bits to voltage levels of one or more memory cells based on a plurality of embedding parameters, program the set of information bits into the one or more memory cells based on the mapping, detect the voltage levels of the one or more memory cells to generate one or more detected voltage levels, and identify a set of predicted information bits based on the one or more detected voltage levels using a neural network comprising a plurality of network parameters, wherein the network parameters are trained together with the embedding parameters.

Abstract: Hierarchical coding architectures and schemes based on multistage concatenated codes are described. For instance, multiple encoder and decoder hierarchies may be implemented along with use of corresponding stages of concatenated codes. The coding scheme generally includes an inner coding scheme (e.g., a polar coding scheme, such as a hybrid polar code or Bose Chaudhuri and Hocquenghem (BCH) code), an outer coding scheme (e.g., a Reed-Solomon (RS) coding scheme), and one or more middle coding schemes. The inner coding scheme is based on a polarization transformation (e.g., polar codes with cyclic redundancy check (CRC) codes, polar codes with dynamic freezing codes, polarization-adjusted convolutional (PAC) codes, etc.) which allows for embedding parity data from an outer code inside a codeword along with the user data. The outer coding scheme has a similar concatenated structure (e.g., of an inner RS code with an outer RS code).

Abstract: A memory system includes a memory device and a memory controller. The memory device includes a plurality of memory cells. The memory controller is configured to manage the memory device using a cell level assignment with respect to a plurality of memory cell levels, determine a cell count for each of the cell levels associated with original data of the memory device that is to be accessed, predict an error rate from the cell counts, and selectively adjust the cell level assignment based on the error rate.

Abstract: A mobile electronic device may include a memory device and a memory controller including an error correction code (ECC) encoder to encode data, a constrained channel encoder configured to encode an output of the ECC encoder based on one or more constraints, a reinforcement learning pulse programming (RLPP) component configured to identify a programming algorithm for programming the data to the memory device, an expectation maximization (EM) signal processing component configured to receive a noisy multi-wordline voltage vector from the memory device and classify each bit of the vector with a log likelihood ration (LLR) value, a constrained channel decoder configured to receive a constrained vector from the EM signal processing component and produce an unconstrained vector, and an ECC decoder configured to decode the unconstrained vector. A machine learning interference cancellation component may operate based on or independent of input from the EM signal processing component.

Abstract: A method, apparatus, non-transitory computer readable medium, and system for using an error correction code in a memory device with a neural network are described. Embodiments of the method, apparatus, non-transitory computer readable medium, and system may receive a signal from a physical channel, wherein the signal is based on a modulated symbol representing information bits encoded using an error correction coding scheme, extract features from the signal using a feature extractor trained using probability data collected from the physical channel, and decode the information bits with a neural network decoder taking the extracted features as input.

Abstract: A hardware architecture for systematic erasure encoding includes first matrix constructor circuit that receives parity-check matrix H for codeword C, and the erased part of codeword C, and outputs matrix H1 of columns of H located on erased coordinates of code C; second matrix constructor circuit that receives matrix H and the erased part of codeword C and outputs matrix H2 of columns of H located on non-erased coordinates of code C; a neural network that calculates matrix J1 that is an approximate inverse of matrix H1. The matrix J1 is used to determine new erasures in the parity matrix H and new erased coordinates. Matrices H1 and H2 are updated, and the updated H1 is provided as feedback to the first matrix constructor circuit. A calculator circuit restores the erased coordinates of codeword C, from the matrix J1, matrix H2, and a non-erased part of codeword C.

Abstract: A NAND memory device that includes a plurality of blocks, each block comprises a plurality of wordlines and an associated agent, and each wordline comprises a plurality of cells and a plurality of voltage levels and an associated agent, and each voltage level comprises an agent. A method of programming the NAND memory device includes receiving, by an agent at a given rank in the plurality of ranks, parameters from a higher rank agent in the hierarchy of ranks and a state from the memory device; determining, by the agent, an action from the parameters and the state; passing the action as parameters to a lower rank agent in the hierarchy of ranks; and updating the agent based on a reward output by the agent, wherein the reward measures a difference between the target voltage levels of the cells and the actual voltage levels programmed to the cells.

Abstract: A memory system includes a memory device and a memory controller. The memory device includes a plurality of memory cells. The memory controller includes an error correction code (ECC) circuit. The ECC circuit is configured to determine data rows of first write data that are not all zeros and store the determined data rows in buffer rows of a buffer along with corresponding row indexes. The memory controller is configured to write second data based on the buffer to the memory device.

Abstract: Systems and methods of the present disclosure may be used to improve equalization module architectures for NAND cell read information. For example, embodiments of the present disclosure may provide for de-noising of NAND cell read information using a Multiple Shallow Threshold-Expert Machine Learning Models (MTM) equalizer. An MTM equalizer may include multiple shallow machine learning models, where each machine learning model is trained to specifically solve a classification task (e.g., a binary classification task) corresponding to a weak decision range between two possible read information values for a given NAND cell read operation. Accordingly, during inference, each read sample with a read value within a weak decision range is passed through a corresponding shallow machine learning model (e.g., a corresponding threshold expert) that is associated with (e.g., trained for) the particular weak decision range.

Abstract: A method of performing division operations in an error correction code includes the steps of receiving an output ??F†{0} wherein F=GF(2r) is a Galois field of 2r elements, ?=?0?i?r?1?i×?i wherein ? is a fixed primitive element of F, and ?i?GF(2), wherein K=GF(2s) is a subfield of F, and {1, ?} is a basis of F in a linear subspace of K; choosing a primitive element ??K, wherein ?=?1+?×?2, ?1=?0?i?s?1 ?i×?i?K, ?2=?0?i?s?1 ?i+s×?i?K, and ?=[?0, . . . , ?r?1]T?GF(2)r; accessing a first table with ?1 to obtain ?3=?1?1, computing ?2×?3 in field K, accessing a second table with ?2=?3 to obtain (1+?×?2×?3)?1=?4+?×?5, wherein ??1=(?1×(1+?×?2×?3))?1=?3×(?4+?×?5)=?3×?4+?×?3×?5; and computing products ?3×?4 and ?3×?5 to obtain ??1=?0?i?s?1?i×?i+?·?i?i?s?1?i+s=?i where ?i?GF(2).

Abstract: A memory system includes a memory device and a memory controller. The memory device includes a plurality of memory cells. The memory controller is configured to manage the memory device using a cell level assignment with respect to a plurality of memory cell levels, determine a cell count for each of the cell levels associated with original data of the memory device that is to be accessed, predict an error rate from the cell counts, and selectively adjust the cell level assignment based on the error rate.

Abstract: Embodiments of the present disclosure provide a controller hierarchical decoding architecture. For instance, multiple decoder hierarchies are implemented along with use of hierarchies of codes with locality (e.g., larger code length of a hierarchy is composed of local codes from a lower hierarchy). The hierarchical Error Correction Code (ECC) decoding includes multiple hierarchies such as a first hierarchy, a second hierarchy, and additional hierarchies as needed. A first hierarchy includes low-complexity ECC engines, each connected to a NAND channel for computing local codes of low code lengths. A second hierarchy includes higher complexity ECC engines that shares several NAND channels for correcting corrupt data using relatively larger code length (e.g., and the higher complexity ECC engines of the second hierarchy performs decoding operations using more complex decoding algorithms). The larger code length is composed of local codes from a previous hierarchy.

Abstract: A machine-learning (ML) error-correcting code (ECC) controller may include a hard-decision (HD) ECC decoder optimized for high-speed data throughput, a soft-decision (SD) ECC decoder optimized for high-correctability data throughput, and a machine-learning equalizer (MLE) configured to variably select one of the HD ECC decoder or the SD ECC decoder for data throughput. An embodiment of the ML ECC controller may provide speed-optimized HD throughput based on a linear ECC. The linear ECC may be a soft Hamming permutation code (SHPC).