Apple Inc.

Moti Teitel

Micha Anholt

Tomer Ish-Shalom

Yonathan Tate

Naftali Sommer

Eyal Gurgi

Barak Baum

Maya Barkon

Moshe Neerman

Meir Dalal

Asaf Landau

A method for data encoding includes receiving a data vector to be encoded into a code word in accordance with a code defined by a parity-check matrix H. An intermediate vectoris produced by multiplying the data vector by a data sub-matrix Hof the parity-check matrix H. A parity part of the code word is derived by applying a sequence of operations to the intermediate vectorbased on a decomposition of a parity sub-matrix Hof the matrix H using matrices A, C, U and V, in which decomposition A is a block triangular matrix that has the same size as H, C is matrix that is smaller than H, and the matrices U and V are placement matrices that are selected so that A, C, U and V satisfy a matrix equation H=A+UCV.

Data encoding by efficient inversion of a parity-check sub-matrix

An apparatus includes an interface, main and secondary processing modules, and circuitry. The interface is configured to receive input data to be processed in accordance with a GLDPC code defined by a parity-check-matrix including multiple sub-matrices, each sub-matrix including a main diagonal and one or more secondary diagonals, and each of the main and secondary diagonals includes N respective block matrices. The main processing module is configured to calculate N first partial syndromes based on the input data and on the block matrices of the main diagonals. The secondary processing module is configured to calculate N second partial syndromes based on the input data and on the block matrices of the secondary diagonals. The circuitry is configured to produce N syndromes by respectively combining the N first partial syndromes with the N second partial syndromes, and to encode or decode the input data, based on the N syndromes.

Efficient syndrome calculation in processing a GLDPC code

A decoder includes one or more Variable-Node Processors (VNPs) that hold respective variables, and logic circuitry. The logic circuitry is configured to decode a code word of an Error Correction Code (ECC), which is representable by a set of check equations, by performing a sequence of iterations such that each iteration involves processing of at least some of the variables, to hold one or more auxiliary equations derived from the check equations, so that a number of the auxiliary equations is smaller than a number of the check equations, to evaluate the auxiliary equations, during the sequence of iterations, using the variables, and, in response to detecting that the variables satisfy the auxiliary equations, to terminate the sequence of iterations and output the variables as the decoded code word.

Efficient convergence in iterative decoding

A decoder includes circuitry and a soft decoder. The circuitry is configured to receive channel hard decisions for respective bits of a Generalized Low-Density Parity Check (GLDPC) code word that includes multiple component code words, including first and second component code words having one or more shared bits, to schedule decoding of the GLDPC code word, and following the decoding, to output the decoded GLDPC code word. The soft decoder is configured to receive the channel hard decisions corresponding to the first component code word, to further receive soft reliability measures that were assigned to the shared bits in decoding the second component code word, and to decode the first component code word based on the channel hard decisions and the soft reliability measures.

GLDPC soft decoding with hard decision inputs

A storage device includes a memory that includes storage circuitry and a memory including multiple memory cells. The storage circuitry is configured to store in a group of the memory cells data that was encoded using an error correcting code (ECC) consisting of multiple component codes, to define multiple threshold settings, each specifying positions of one or more reading-thresholds, to read the data from the memory cells in the group using the threshold settings and decode the read data using the component codes, to calculate for the component codes respective component-code scores that are indicative of levels of confidence in the decoded data of the component-codes, to select, based on the component-code scores, a threshold setting that is expected to result in a best readout performance among the multiple threshold settings, and to read data from the memory using the selected threshold setting.

Reading-threshold setting based on data encoded with a multi-component code

A method includes receiving a first element of a Galois Field of order q, where q is a prime number and m is a positive integer. The first element is raised to a predetermined power so as to form a second element z, wherein the predetermined power is a function of qand an integer p, where p is a prime number which divides q&#x2212;1. The second element z is raised to a ppower to form a third element. If the third element equals the first element, the second element multiplied by a proot of unity raised to a respective power selected from a set of integers between 0 and p&#x2212;1 is output as at least one root of the first element.

Cubic root of a galois field element

An apparatus for data coding includes an encoder and a decoder. The encoder is configured to receive input data including one or more m-bit data groups that are associated with respective group indices, to generate a code word that includes the input data and an m-bit redundancy that depends on the data groups and on the respective group indices, and to send the code word over a channel. The decoder is connected to the channel and is configured to produce a syndrome that equals zero when the code word is error-free, and when the code word contains a single error caused by the channel, is indicative of an erroneous group in which the single error occurred, and of a location of the single error within the erroneous group, and to recover the input data by correcting the single error at the location in the erroneous group.

Efficient coding with single-error correction and double-error detection capabilities

A method includes storing data encoded with an ECC in a group of memory cells by writing respective storage values to the memory cells. Multiple sets of readout results are read from the memory cells by comparing the storage values to one or more threshold combinations, each including multiple read thresholds. A plurality of partial syndromes of the ECC is computed, each partial syndrome computed over the readout results that were read using a respective threshold combination. A respective syndrome is calculated for each threshold combination, in at least a subset of all possible threshold combinations, based on one or more of the partial syndromes associated with that threshold combination. A preferred threshold combination is selected, from among the threshold combinations, for which a weight of the respective syndrome is minimal, by processing less than all the partial syndromes associated with all the possible threshold combinations.

Efficient search for optimal read thresholds in flash memory

A method for Error Correction Code (ECC) encoding includes receiving data to be encoded. The data is encoded to produce a composite code word that includes multiple component code words. Each component code word in at least a subset of the component code words is encoded in accordance with a respective component code and has at least one respective bit in common with each of the other component code words.

Error correction coding with high-degree overlap among component codes

A method for data storage includes reading storage values, which represent stored data, from a group of memory cells using read thresholds, and deriving respective soft reliability metrics for the storage values. The storage values are classified into two or more subgroups based on a predefined classification criterion. Independently within each subgroup, a subgroup-specific distribution of the storage values in the subgroup is estimated, and the soft reliability metrics of the storage values in the subgroup are corrected based on the subgroup-specific distribution. The stored data is decoded using the corrected soft reliability metrics.

Correcting soft reliability measures of storage values read from memory cells

A method, including factoring an order of a multiplicative group of a Galois Field to produce a first integer factor p and a second integer factor q, wherein the multiplicative group includes (2&#x2212;1) elements, m a non-negative integer, so that 2&#x2212;1=pq. The method further includes receiving an element x of the Galois Field expressible as &#x3b1;, where &#x3b1; is a primitive element of the group, i is a first non-negative integer less than p, and j is a second integer less than q. An inverse or a logarithm of the element x is calculated as a function of qi and j.

Implementation of log and inverse operation in a Galois Field

A method for decoding includes receiving channel inputs for respective bits of a super code word that includes at least first and second component code words having a shared group of bits. At least the first and second component code words are iteratively decoded, and, in response to recognizing that the first and second component code words contain errors only within the shared group of bits, the first and second component code words are jointly decoded.

Decoding a super-code using joint decoding of underlying component codes

A method for data storage includes, in a first programming phase, storing first data in a group of memory cells by programming the memory cells in the group to a set of initial programming levels. In a subsequent second programming phase, second data is stored in the group by identifying the memory cells in the group that were programmed in the first programming phase to respective levels in a predefined partial subset of the initial programming levels, and programming only the identified memory cells with the second data, so as to set at least some of the identified memory cells to one or more additional programming levels that are different from the initial programming levels. The memory cells to which the second data was programmed are recognized by reading only a partial subset of the first data. The second data is read from the recognized memory cells.

Data storage management in analog memory cells using a non-integer number of bits per cell

A method, in a memory including multiple analog memory cells, includes segmenting a group of the memory cells into a common section and at least first and second dedicated sections. Each dedicated section corresponds to a read threshold that is used for reading a data page to be stored in the group. Data to be stored in the group is jointly balanced over a union of the common section and the first dedicated section, and over the union of the common section and the second dedicated section, to create a balanced page such that for each respective read threshold an equal number of memory cells will be programmed to assume programming levels that are separated by the read threshold. The balanced page is stored to the common and dedicated sections, and the read thresholds are adjusted based on detecting imbalance between data values in readout results of the balanced page.

Threshold adjustment using data value balancing in analog memory device

A method includes reading a group of analog memory cells using first explicit read thresholds, to produce first readout results. The group is re-read using second explicit read thresholds, to produce second readout results. The group is read using one or more sets of auxiliary thresholds so as to produce auxiliary readout results, such that the number of the auxiliary thresholds in each set is the same as the number of the first explicit read thresholds and the same as the number of the second explicit read thresholds. A readout performance of third read thresholds, which include at least one of the first explicit read thresholds and at least one of the second explicit read thresholds, is evaluated using the first, second and auxiliary readout results.

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Tel Aviv, Israel

Moti Teitel