Abstract: A method includes initiating a decoding operation of a first portion of a codeword representation to generate a set of data bits. The first portion includes first parity bits and is associated with a first error correcting code. The method includes initiating an encoding operation of the set of data bits according to a second error correcting code to generate computed parity bits. The method includes comparing the computed parity bits to a second portion of the codeword representation to determine a number of bits that differ between the computed parity bits and the second portion of the codeword representation. The method also includes generating an indication of successful decoding in response to the number of bits that differ being less than a threshold value.

Abstract: Bits are stored by attempting to set parameter value(s) of (a) cell(s) to represent some of the bits. In accordance with the attempt, an adaptive mapping of the bits to value ranges is provided and the value(s) is/are adjusted accordingly as needed. Or, to store (a) bit(s) in (a) cell(s), a default mapping of the bit(s) to a predetermined set of value ranges is provided and an attempt is made to set the cell value(s) accordingly. If, for one of the cells, the attempt sets the value such that the desired range is inaccessible, an adaptive mapping is provided such that the desired range is accessible. Or, to store (a) bit(s) in (a) cell(s), several mappings of the bit(s) to a predetermined set of ranges is provided. Responsive to an attempt to set the cell value(s) according to one of the mappings, the mapping to actually use is selected.

Abstract: To store bits in one or more cells, an adaptive mapping of bits to ranges of a physical parameter of the cell(s) is provided, in accordance with respective initial values of the physical parameter, by steps including encoding the bits as a codeword by partitioning the bits into subsets and finding a factor bit string such that the codeword is a concatenation of the factor bit string and separate Galois field products of all the subsets with the factor bit string. The initial values of the physical parameter are adjusted accordingly as needed.

Abstract: To decode a representation of a codeword that encodes K information bits as N>K codeword bits, messages are exchanged between N bit nodes and N?K check nodes of a graph in which E edges connect the bit nodes and the check nodes. While messages are exchanged, fewer than E of the messages are stored, and/or fewer than N soft estimates of the codeword bits are stored. In some embodiments, the messages are exchanged only within sub-graphs and between the sub-graphs and one or more external check nodes. While messages are exchanged, the largest number of stored messages is the number of edges in the sub-graph with the most edges plus the number of edges that connect the sub-graphs to the external check node(s), and/or the largest number of stored soft estimates is the number of bit nodes in the sub-graph with the most bit nodes.

Abstract: Data that are stored in cells of a multi-bit-per cell memory, according to a systematic or non-systematic ECC, are read and corrected (systematic ECC) or recovered (non-systematic ECC) in accordance with estimated probabilities that one or more of the read bits are erroneous. In one method of the present invention, the estimates are a priori. In another method of the present invention, the estimates are based only on aspects of the read bits that include significances or bit pages of the read bits. In a third method of the present invention, the estimates are based only on values of the read bits. Not all the estimates are equal.

Abstract: A method includes a first encoding operation associated with a first algebraic error correcting code generating a first set of first parity bits corresponding to a first set of information bits and a second set of first parity bits corresponding to a second set of information bits. A second encoding operation associated with a second algebraic error correcting code generates a first set of second parity bits corresponding to the first set of information bits and a second set of second parity bits corresponding to the second set of information bits. A third encoding operation generates a set of joint parity bits. The first set of information bits, the second set of information bits, the first set of first parity bits, the second set of first parity bits, and the joint parity bits may be stored in a data storage device as a single codeword.

Abstract: A termination indication is computed during an iteration of an iterative decoding of a representation of a codeword according to a schedule. The termination indication is tested to see if the decoding has converged or is not likely to converge. The testing of the termination indication shows convergence or lack of likelihood thereof even if a codeword bit estimate was flipped during an immediately preceding traversal of the schedule. Preferably, the termination indication includes an error correction syndrome weight, a zero value whereof indicates convergence, and the computing of the termination indication includes, in response to the flipping of a codeword bit estimate, flipping the error correction syndrome bits that are influenced by that codeword bit estimate.

Abstract: A method and system for optimizing flash memory without dedicated parity area and with reduced array size. The memory size of a multi level cell (MLC) flash is reduced and controller operation is simplified. Simplified operation includes the controller being able to program each host data page to an integer number of flash pages. A maximal available information bits per cell (IBPC) is maintained in a flash device while also maximizing the programming throughput of the flash. Features include the ability to dynamically select which number of cell states is used by flash memory cells.

Abstract: A memory system is disclosed. The system comprises a memory layer between a first layer and a second layer, wherein the first layer and the second layer are configured to apply an electrical bias to the memory layer. In some embodiments the memory layer comprises nanodots made of a material selected from the group consisting of peptides and amino acids.

Abstract: k input bits are encoded according to a code with which is associated a m×n=m+k parity check matrix H. The resulting codeword is punctured, with n?<n bits. The punctured codeword is exported to a corrupting medium such as a communication channel or a memory. A representation of the punctured codeword is imported from the corrupting medium and is decoded using a matrix H? that is smaller than H. For example, H has at most m rows and fewer than n columns but more than n? columns.

Abstract: k input bits are encoded according to a code with which is associated a m×n=m+k parity check matrix H. The resulting codeword is punctured, with n?<n bits. The punctured codeword is exported to a corrupting medium such as a communication channel or a memory. A representation of the punctured codeword is imported from the corrupting medium and is decoded using a matrix H? that is smaller than H. For example, H has fewer than m?=m?(n?n?) rows and fewer than n? columns.

Abstract: To decode a representation, imported from a channel, of a codeword that encodes K information bits as N>K codeword bits, estimates of the codeword bits are updated by exchanging messages between N bit nodes and N?K check nodes of a graph in a plurality of iterations. In each of one or more of the iterations, some or all values associated with the bit nodes, and/or some or all values associated with check nodes, and/or some or all messages are modified in a manner that depends explicitly on the ordinality of the iteration and is independent of any other iteration. Alternatively, the modifications are according to respective locally heteromorphic rules.

Abstract: A codeword is decoded by receiving a codeword representation that includes a plurality of soft bits and iteratively updating the soft bits. Whether each soft bit participates in at least some iterations is determined according to a selection criterion, e.g., probabilistically, or according to iteration number, or according to the soft bit's iteration history. For example, each soft bit might participate in some or all iterations with a probability that is a function of both the iteration number and a reliability measure of that soft bit. Preferably, the iterations are LDPC iterations in which variable nodes are addressed sequentially for exchanging messages with corresponding check nodes.

Abstract: Input bits are stored in memory cells by mapping the input bits into a larger number of transformed bits using a shaping encoding that has a downward asymptotic bias with respect to a mapping of bit patterns to cell states and programming some of the cells according to that mapping of bit patterns to cell states. The programmed cells are erased before being programmed to store any other bits. The invention sacrifices memory capacity to increase endurance.

Abstract: A method includes initiating a decoding operation of a first portion of a codeword to generate a set of data bits. The first portion includes first parity bits and is associated with a first error correcting code. The method includes initiating an encoding operation of the set of data bits according to a second error correcting code to generate computed parity bits. The method includes comparing the computed parity bits to a second portion of the codeword to determine a number of bits that differ between the computed parity bits and the second portion of the codeword. The method also includes generating an indication of successful decoding in response to the number of bits that differ being less than a threshold value.

Abstract: A method includes a first encoding operation associated with a first algebraic error correcting code generating a first set of first parity bits corresponding to a first set of information bits and a second set of first parity bits corresponding to a second set of information bits. A second encoding operation associated with a second algebraic error correcting code generates a first set of second parity bits corresponding to the first set of information bits and a second set of second parity bits corresponding to the second set of information bits. A third encoding operation generates a set of joint parity bits. The first set of information bits, the second set of information bits, the first set of first parity bits, the second set of first parity bits, and the joint parity bits may be stored in a data storage device as a single codeword.

Abstract: A plurality of information bits are encoded using a parity-check matrix that is equivalent to a modular code matrix. The modular code matrix is a diagonal sub-matrix structure immediately above a connection layer that includes a plurality of diverse connection layer sub-matrices, all but at most one of which are below corresponding diagonal matrix structure sub-matrices. The information bits are assembled with a plurality of parity bits produced by the encoding to provide a codeword that is exported to a medium. Preferably, all the diagonal matrix structure sub-matrices are identical. Preferably, some of the parity bits are computed using only diagonal matrix structure sub-matrices.

Abstract: To read memory cells that have been programmed to store an ECC codeword, with each cell storing a respective plurality of bits of the codeword, a respective value of an operational parameter such as a threshold voltage of each cell is measured. Each bit is assigned a respective metric, such as a LLR estimate of the bit, based at least in part on the respective value of the operational parameter of the bit's cell. The metrics are decoded with reference both to the ECC and to mutual constraints of the metrics within each cell that are independent of the ECC.

Abstract: To read a plurality of memory cells, each cell is assigned to a respective cell population. A respective value of an operational parameter of each cell is measured. Each cell is assigned an a-priori metric based at least in part on one or more CVD parameter values of the cell's population. The a-priori metrics are decoded. Based at least in part on the resulting a-posteriori metrics, the CVD parameter values are corrected, without repeating the measurements of the cell operational parameter values. The operational parameter values are indicative of bit patterns stored in the cells, and the correction of the CVD parameter values is constrained by requiring the bit patterns collectively to be a valid codeword.

Abstract: To decode a manifestation of a codeword in which K information bits are encoded as N>K codeword bits, messages are exchanged between N bit nodes and N?K check nodes. During computation, messages are expressed with a full message length greater than two bits. In each iteration, representations of at least some of the exchanged messages are stored. For at least one node, if representations of messages sent from that node are stored, then the representation of one or more of the messages is stored using at least two bits but using fewer bits than the full message length, and the representation of one other message is stored with full message length. Preferably, the messages that are stored using fewer bits than the full message length are messages sent from check nodes.