Abstract: 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.

Abstract: A decoder includes an interface and circuitry. The interface is configured to receive a code word that was encoded using a Quasi-Cyclic Low Density Parity Check (QC-LDPC) Error Correcting Code (ECC) represented by multiple check equations that are defined over multiple variables. The circuitry is configured to decode the code word by iteratively processing multiple layers that each includes a respective subset of the variables of the code word, and producing per each layer one or more count updates, and to generate a total number of errors corrected over the entire code word by accumulating the count updates.

Abstract: A decoder includes variable-node circuitry, check-node circuitry and a Message Passing (MP) module, which includes multiple configurable partial cyclic shifters that each supports only a partial subset of shift values out of a full range of shift values 0 . . . L?1. The variable-node circuitry and check-node circuitry are configured to exchange messages with one another in accordance with a parity check matrix that represents a respective Quasi-Cyclic (QC)-Low Density Parity Check (LDPC) Error Correcting Code (ECC) and that includes L-by-L sub-matrices, and to process the exchanged messages to decode a given code word that was encoded using the QC-LDPC ECC. The MP module is configured to schedule the variable-node circuitry and check-node circuitry that are interconnected in accordance with a respective sub-matrix to exchange L messages simultaneously by assigning a given partial cyclic shifter to shift the L messages cyclically a number of positions that depends on a structure of the respective sub-matrix.

Abstract: 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.

Abstract: 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 vector s is produced by multiplying the data vector by a data sub-matrix Hs of the parity-check matrix H. A parity part of the code word is derived by applying a sequence of operations to the intermediate vector s based on a decomposition of a parity sub-matrix Hp of 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 Hp, C is matrix that is smaller than Hp, and the matrices U and V are placement matrices that are selected so that A, C, U and V satisfy a matrix equation Hp=A+UCV.

Abstract: A decoder includes variable-node circuitry, check-node circuitry and a Message Passing (MP) module, which includes multiple configurable partial cyclic shifters that each supports only a partial subset of shift values out of a full range of shift values 0 . . . L?1. The variable-node circuitry and check-node circuitry are configured to exchange messages with one another in accordance with a parity check matrix that represents a respective Quasi-Cyclic (QC)-Low Density Parity Check (LDPC) Error Correcting Code (ECC) and that includes L-by-L sub-matrices, and to process the exchanged messages to decode a given code word that was encoded using the QC-LDPC ECC. The MP module is configured to schedule the variable-node circuitry and check-node circuitry that are interconnected in accordance with a respective sub-matrix to exchange L messages simultaneously by assigning a given partial cyclic shifter to shift the L messages cyclically a number of positions that depends on a structure of the respective sub-matrix.