Abstract: Systems, devices, and methods for encoding information bits for storage, including obtaining information bits; encoding the information bits using an inner code to obtain a plurality of inner code words; encoding the plurality of inner code words using an outer code to generate an outer code word; and storing the outer code word in a storage device, wherein at least one of the inner code and the outer code includes a generalized concatenated code (GCC), and wherein the outer code word includes a hierarchical-GCC (H-GCC) code word.

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. A meta network may generate parameters for each of the shallow machine learning models such that each shallow machine learning model may be able to 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 may be passed through a corresponding shallow machine learning model (e.g., a corresponding threshold expert) that is associated with the particular weak decision range.

Abstract: A method for soft decoding of generalized Reed-Solomon (RS) error correction codes, includes receiving a codeword through a digital electronic communication channel; verifying that an HD error-and-erasures decoding has failed; finding a Groebner basis that accounts for a fixed set of erasures; constructing a Chase and GMD decoding tree on the set of Chase coordinates and the set of GMD coordinates; traversing the decoding tree using polynomials of the Groebner basis as a basis that represents updated coefficient polynomials on the Chase and GMD decoding tree; updating polynomials on the decoding tree using root and derivate steps that flip an edge, or a root step for an erasure edge; calculating error locations by polynomial evaluation of candidate polynomials from the decoding tree, and calculating error values by using Forney's formula; and correcting the received codeword according to the calculated error locations and calculated error values.

Abstract: A hardware circuit for calculating syndromes in Reed-Solomon (RS) error correction codes comprises a plurality of p multiplexors, where p is a positive integer, where each multiplexor receives ?{circumflex over (?)}i powers that are selected by j, wherein ? is a primitive point of a RS generator polynomial and j is an index of an RS symbol, where i and j are positive integers, where 1?i?p, and outputs ?{circumflex over (?)}(i×j); and a plurality of p first multipliers, where each first multiplier is associated with a multiplexor and receives ?{circumflex over (?)}(i×j) from the associated multiplexor, multiplies the ?{circumflex over (?)}(i×j) by a jth RS-word symbol Rj and outputs Rj×?{circumflex over (?)}(i×j). The hardware circuit calculates and outputs p products of the form Rj×?{circumflex over (?)}(i×j), wherein 1?i?p.

Abstract: Systems, devices, and methods for encoding information bits for storage, including obtaining information bits and a target constraints vector, placing the information bits in an input vector, setting balance bits included in the input vector to zero, encoding the input vector using a systematic code to obtain a preliminary codeword, applying a constraints matrix to the preliminary codeword to obtain a preliminary constraints vector, applying a transition matrix to a sum of the preliminary constraints vector and the target constraints vector to determine updated balance bits, obtaining an output codeword based on the information bits and the updated balance bits, and storing the output codeword in the storage device.

Abstract: A method for accelerating computational storage in an all-flash-array that comprises a plurality of solid state drives (SSDs) connected in a ring topology. The method includes receiving, by a controller of a first SSD, a request to read or write data from a dynamic random access memory (DRAM) associated with the first SSD, creating a packet that includes an identifier for the first SSD in the ring topology, an identifier for the packet, and a read/write flag that identifies the request, and transmitting the packet to a next SSD in the ring topology. When the request is a read request and a read data address is not located in the DRAM, the read/write flag indicates a read-request, and when the request is a write request and the DRAM is full, the read/write flag indicates a write-request, and the packet includes data to be written.

Abstract: Systems, devices, and methods for decoding information bits obtained from storage, including obtaining a frame corresponding to a codeword from the storage device, performing a first decoding operation on the frame, based on the first decoding operation indicating that a number of errors is greater than a predetermined number, selecting at least one potential error bit, and perform a second decoding operation based on the at least one potential error bit, based on the second decoding operation indicating that the number of errors is not equal to the predetermined number plus one, determining that the frame is not correctable by the first decoding operation and the second decoding operation, and based on the second decoding operation indicating that the number of errors is equal to the predetermined number plus one, correcting the frame based on a result of the second decoding operation to obtain a corrected frame, and obtaining information bits corresponding to the codeword based on the corrected frame.

Abstract: Systems, devices, and methods for decoding information bits obtained from storage, including obtaining a plurality of data symbols; providing the plurality of data symbols to a neural network; obtaining a plurality of threshold voltage targets based on an output of the neural network; and programming the plurality of data symbols to a plurality of memory cells included in a storage device based on the plurality of threshold voltage targets.

Abstract: Provided are a memory system, a method of reading data and a method of finding read thresholds. The method of finding read thresholds includes: selecting a channel distribution among a plurality of channel distributions that corresponds to a read page of the memory device to be read in response to a read command; generating a Trellis diagram based on a decoding scheme and a type of the read page; determining an optimal path through the Trellis diagram using the selected channel distribution according to a dynamic programming algorithm; and finding the read thresholds from the optimal path.

Abstract: A method of simplified successive cancellation list (SSCL) error decoding of S-polar codes includes representing an S-polar code as a perfect binary tree; providing a node v a vector ?v(l) of soft information from a parent node; computing a vector ?vl(l) of soft information for a left child of node v; providing node v with a vector ?vl(l) of hard decisions from the left child and using it with ?v(l) to create a soft information vector ?vr(l) and passing it to a right child of node v; providing node v with a vector ?vr(l) of hard decisions from its right child and using it with ?vl(l) to create a hard decision vector, ?v of hard decisions, and passing it to its parent node; updating, when v is a ith leaf of the perfect tree, two path metrics, and selecting paths obtained by expanding current paths with a lowest path metric.

Abstract: Systems, devices, and methods for encoding information bits for storage, including obtaining information bits; encoding the information bits using an inner code to obtain a plurality of inner code words; encoding the plurality of inner code words using an outer code to generate an outer code word; and storing the outer code word in a storage device, wherein at least one of the inner code and the outer code includes a generalized concatenated code (GCC), and wherein the outer code word includes a hierarchical-GCC (H-GCC) code word.

Abstract: Systems, devices, and methods for decoding information bits obtained from storage, including obtaining a codeword from among a plurality of codewords stored in a storage device, wherein the codeword includes a plurality of frames; obtaining an initial error locator polynomial (ELP) corresponding to the codeword; decoding a frame of the plurality of frames; based on determining that the frame is successfully decoded, determine an updated ELP based on the initial ELP and information about the frame; and obtaining information bits corresponding to the codeword based on the updated ELP, wherein the updated ELP includes a plurality of updated coefficients, and wherein the updated ELP is determined by simultaneously calculating at least two updated coefficients from among the plurality of updated coefficients.

Abstract: A method of operation for a Reed-Solomon decoder includes receiving partial input data of symbols of a Reed-Solomon codeword; updating Reed-Solomon syndromes and error location polynomial coefficients based on the partial input data; maintaining the Reed-Solomon syndromes and the error location polynomial coefficients in a memory prior to starting activation of Reed-Solomon decoding; and inputting the Reed-Solomon syndromes and the error location polynomial coefficients to a first activation of Reed-Solomon decoding including calculating an initial error evaluator polynomial as a first error evaluator polynomial, performing error detection based on the first error evaluator polynomial to determine presence and location of errors in an input Reed-Solomon codeword, and updating the error location polynomial when errors are found in the input Reed-Solomon codeword.

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. A meta network may generate parameters for each of the shallow machine learning models such that each shallow machine learning model may be able to 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 may be passed through a corresponding shallow machine learning model (e.g., a corresponding threshold expert) that is associated with the particular weak decision range.

Abstract: Systems, devices, and methods for decoding information bits obtained from storage, including obtaining a frame corresponding to a codeword from the storage device, performing a first decoding operation on the frame, based on the first decoding operation indicating that a number of errors is greater than a predetermined number, selecting at least one potential error bit, and perform a second decoding operation based on the at least one potential error bit, based on the second decoding operation indicating that the number of errors is not equal to the predetermined number plus one, determining that the frame is not correctable by the first decoding operation and the second decoding operation, and based on the second decoding operation indicating that the number of errors is equal to the predetermined number plus one, correcting the frame based on a result of the second decoding operation to obtain a corrected frame, and obtaining information bits corresponding to the codeword based on the corrected frame.

Abstract: Systems, devices, and methods for decoding information bits obtained from storage, including obtaining a codeword from among a plurality of codewords stored in a storage device, wherein the codeword includes a plurality of frames; obtaining an initial error locator polynomial (ELP) corresponding to the codeword; decoding a frame of the plurality of frames; based on determining that the frame is successfully decoded, determine an updated ELP based on the initial ELP and information about the frame; and obtaining information bits corresponding to the codeword based on the updated ELP, wherein the updated ELP includes a plurality of updated coefficients, and wherein the updated ELP is determined by simultaneously calculating at least two updated coefficients from among the plurality of updated coefficients.

Abstract: A method of correcting data stored in a memory device includes: applying an iterative decoder to the data; determining a total number of rows in first data the decoder attempted to correct; estimating first visible error rows among the total number that continue to have an error after the attempt; estimating residual error rows among the total number that no longer have an error after the attempt; determining second visible error rows in second data of the decoder that continue to have an error by permuting indices of the residual error rows according to a permutation; and correcting the first data using the first visible error rows.

Abstract: Systems, devices, and methods for encoding information bits for storage, including obtaining information bits and a target constraints vector, placing the information bits in an input vector, setting balance bits included in the input vector to zero, encoding the input vector using a systematic code to obtain a preliminary codeword, applying a constraints matrix to the preliminary codeword to obtain a preliminary constraints vector, applying a transition matrix to a sum of the preliminary constraints vector and the target constraints vector to determine updated balance bits, obtaining an output codeword based on the information bits and the updated balance bits, and storing the output codeword in the storage device.

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).

Abstract: Systems, devices, and methods for encoding information bits for storage, including obtaining an information vector comprising a plurality of information bits, a static frozen vector comprising a plurality of static frozen bits, and a constraints vector which indicates at least one constraint; partitioning the information vector into a first information vector and a second information vector; partitioning the static frozen vector into a first static frozen vector and a second static frozen vector; determining an input vector by applying a plurality of matrix operations to the first information vector, the second information vector, the first static frozen vector, the second static frozen vector, and the constraints vector; computing an output codeword of a polar subcode based on the input vector; and transmitting the output codeword to the storage device.