Abstract: In one exemplary embodiment of the invention, a method includes: receiving a first description for a circuit whose operation over a plurality of inputs is to be verified; receiving a second description for expected behavior of the circuit, where the expected behavior in the second description is expressed as a set of algebraic systems of multivariable polynomials over at least one Galois field; applying at least one computational algebraic geometry technique to a combination of the first description and the second description to determine whether the circuit is verified, where verification of the circuit confirms that at least one output obtained based on the first description corresponds to at least one expected value based on the expected behavior expressed in the second description; and outputting an indication as to whether the circuit is verified.

Abstract: Adaptive endurance coding including a method for accessing memory that includes retrieving a codeword from a memory address. The codeword is multiplied by a metadata matrix to recover metadata for the codeword. The metadata includes a data location specification. The data in the codeword is identified in response to the metadata and the data is output as read data.

Abstract: Channel marking is provided in a memory system that includes a first memory channel, a second memory channel, and error correction code (ECC) logic. The memory system is configured to perform a method that includes receiving a request to apply a first channel mark to the first memory channel and determining a priority level of the first channel mark. A request is received to apply a second channel mark to the second memory channel, and a priority level of the second mark is determined. It is determined that the priority level of the first channel mark is higher than the priority level of the second channel mark. The first channel mark is supplied to the ECC logic while blocking the second channel mark from the ECC logic.

Abstract: Channel marking is provided in a memory system that includes a memory channel with a plurality of memory devices. The memory devices are arranged into a first group of memory devices and a second group of memory devices. The memory system is configured to perform a method that includes determining that more than a threshold number of memory devices in the first group are failing. An error correction code (ECC) is configured to compensate for errors associated with memory devices in the first group on the memory channel and to perform error correction on errors associated with memory devices in the second group on the memory channel.

Abstract: Providing increased capacity in heterogeneous storage elements including a method for reading from memory. The method includes receiving a read word from a block of memory cells, where physical characteristics of the memory cells support different sets of data levels. The read word is separated into two or more virtual read vectors. For each of the virtual read vectors, the codebook that was utilized to generate the virtual read vector is identified and a partial read data vector is generated. The generating includes multiplying the virtual read vector by a matrix that represents the codebook. The partial read data vectors are combined into a read message and the read message is output.

Abstract: Error correction and detection in a redundant memory system that includes a memory controller; a plurality of memory channels in communication with the memory controller, the memory channels including a plurality of memory devices; a cyclical redundancy code (CRC) mechanism for detecting that one of the memory channels has failed, and for marking the memory channel as a failing memory channel; and an error correction code (ECC) mechanism. The ECC is configured for ignoring the marked memory channel and for detecting and correcting additional memory device failures on memory devices located on one or more of the other memory channels, thereby allowing the memory system to continue to run unimpaired in the presence of the memory channel failure.

Abstract: Selecting bins in a memory by receiving a target cost for performing writes at an analog memory that is capable of storing a range of values. Possible bins that may be created in the range of values and a cost associated with each possible bin are determined. Each possible bin includes one or more of the values. A group of bins are identified, the group of bins are among the possible bins with associated costs that are within a threshold of the target cost. A maximum number of bins are selected from the group of bins that have non-overlapping values. The selected bins are stored along with the values of the selected bins utilized to encode and decode contents of the analog memory.

Abstract: Constrained coding to reduce floating gate coupling in non-volatile memories including a method for storing data. The method includes receiving write data to be written to a flash memory device, selecting a codeword in response to the write data, and writing the codeword to the flash memory device. The codeword is selected to reduce floating gate coupling in the flash memory device by preventing specified symbol patterns from occurring in the codeword.

Abstract: Error correction in not-and (NAND) flash memory including a system for retrieving data from memory. The system includes a decoder in communication with a memory. The decoder is for performing a method that includes receiving a codeword stored on a page in the memory, the codeword including data and first-tier check symbols that are generated in response to the data. The method further includes determining that the codeword includes errors that cannot be corrected using the first-tier check symbols, and in response second-tier check symbols are received. The second-tier check symbols are generated in response to receiving the data and to the contents of other pages in the memory that were written prior to the page containing the codeword. The codeword is corrected in response to the second-tier check symbols. The corrected codeword is output.

Abstract: Systems and methods are provided that schedule task requests within a computing system based upon the history of task requests. The history of task requests can be represented by a historical log that monitors the receipt of high priority task request submissions over time. This historical log in combination with other user defined scheduling rules is used to schedule the task requests. Task requests in the computer system are maintained in a list that can be divided into a hierarchy of queues differentiated by the level of priority associated with the task requests contained within that queue. The user-defined scheduling rules give scheduling priority to the higher priority task requests, and the historical log is used to predict subsequent submissions of high priority task requests so that lower priority task requests that would interfere with the higher priority task requests will be delayed or will not be scheduled for processing.

Abstract: A phase-change memory (PCM) includes a matrix of storage cells, including at least a first group with at least one cell. Each cell includes a phase change material having at least a first resistance value and a second resistance value, such that the first group can have an identical message encoded therein in at least a first way and a second way. The memory also includes a controller configured to encode the identical message in the at least first group the first or second way, based on which way causes the least amount of writing cost, given current levels of the group. Another embodiment of memory includes a matrix of storage cells. Each of the storage cells has at least two levels, such that each of the storage cells can have an identical message encoded therein in at least a first way and a second way.

Abstract: Performing wear-leveling and bad block management of limited lifetime memory devices. A method for performing wear-leveling in a memory includes receiving logical memory addresses and applying a randomizing function to the logical memory addresses to generate intermediate addresses within a range of intermediate addresses. The intermediate addresses are mapped into physical addresses of a memory using an algebraic mapping. The physical addresses are within a range of physical addresses that include at least one more location than the range of intermediate addresses. The physical addresses are output for use in accessing the memory. The mapping between the intermediate addresses and the physical addresses is periodically shifted. In addition, contents of bad blocks are replaced with redundantly encoded redirection addresses.

Abstract: Techniques for writing to memory using shared address buses. A memory device that includes a plurality of memory arrays connected to a common address bus, the common address bus used to broadcast memory addresses simultaneously to the plurality of memory arrays. Each memory array includes a plurality of memory locations and circuitry for: receiving the broadcasted memory addresses from the address bus; selecting a memory address in the memory array from a list of most recent memory addresses received from the address bus; and performing a memory access at the selected memory address, such that at a given point in time at least two of the memory arrays perform the memory access at a different broadcasted address when the memory access is a write.

Abstract: A phase-change memory (PCM) includes a matrix of storage cells, including at least a first group with at least one cell. Each cell includes a phase change material having at least a first resistance value and a second resistance value, such that the first group can have an identical message encoded therein in at least a first way and a second way. The memory also includes a controller configured to encode the identical message in the at least first group the first or second way, based on which way causes the least amount of writing cost, given current levels of the group. Another embodiment of memory includes a matrix of storage cells, including at least a first group with at least one cell. Each of the storage cells has at least two levels, such that each of the storage cells can have an identical message encoded therein in at least a first way and a second way (the cells can be PCM or another technology).

Abstract: A memory system that includes a plurality of memory arrays having memory cells characterized by a variable write time. The memory system also includes a memory bus configured to receive write commands, and a plurality of data buffers configured to communicate with the memory arrays. The memory system further includes an address buffer configured to communicate with the memory arrays to store the write addresses. A mechanism configured to receive a write command and to split a data line received with the write command into a number of parts is also included in the memory system. The parts of the data line are stored in different data buffers and the writing of the parts of the data line to memory arrays at the write address is initiated. The write command is completed when write completion signals specifying the write address have been received from all of the memory arrays.

Abstract: A data protection method is provided that includes determining a compressibility score of one or more lines of data stored in a memory. The memory includes a first area characterized by a first reliability level and a second area characterized by a second reliability level. Lines of data with a first compressibility score are migrated to the first area of the memory. Lines of data with a second compressibility score are migrated to the second area of the memory.

Abstract: Lossless compression of a data stream having mixed data types, including a method for receiving a data stream that includes a plurality of different types of bit groups. Bit groups of at least two different types are extracted from the data stream to form a sub-stream. Circular shifts of the sub-stream are generated and then sorted into a sorted list of circular shifts. A transformed string that includes a bit group from each of the circular shifts is extracted from the sorted list of circular shifts. A location in the transformed string of a bit group from a pre-determined location in the sub-stream is identified. The transformed string is partitioned between the at least two different types of bit groups into transformed string partitions, and the transformed string partitions are compressed to form compressed transformed string partitions. The compressed transformed string partitions and the location are output.

Abstract: A method for receiving a data stream that includes data samples, each data sample having one of a plurality of actual values. For each data sample in the data stream, a first index in a dictionary is selected. The dictionary includes indices corresponding to each of the plurality of actual values. The first index corresponds to an actual value of the data sample. A predicted value of the data sample is generated in response to previously received data samples in the data stream and to a prediction algorithm. A second index in the dictionary that corresponds to an actual value in the dictionary that is closest to the value of the predicted value is selected. The difference between the first index and the second index is calculated and compressed. The compressed difference between the first index and the second index is then output. This process is performed for each data sample in the data stream.

Abstract: Adaptive write leveling in a memory system that includes a memory that has one or more limited lifetime memory devices and an adaptive write leveling module connected to the memory. The adaptive write leveling module is operative for monitoring a write data stream that includes write line addresses. A property of the write data stream is detected and a write leveling process is adapted in response to the detected property. The write leveling process is applied to the write data stream to generate physical addresses from the write line addresses.

Abstract: Adaptive write leveling in limited lifetime memory devices including performing a method for monitoring a write data stream that includes write line addresses. A property of the write data stream is detected and a write leveling process is adapted in response to the detected property. The write leveling process is applied to the write data stream to generate physical addresses from the write line addresses.