Abstract: A codeword is generated from a message. One or more anchor values are appended to the codeword at predetermined anchor positions. Before the codeword is stored in a memory block, the locations and values of stuck cells in the memory block are determined. Based on the values and positions of the stuck cells, the values of the codeword are remapped so that values of the codeword that are the same as the values of the stuck cells are placed at the positions of the stuck cells. The remapped codeword is stored in the memory block. When the message is later read, the original codeword can be recovered from the remapped codeword based on the locations of the anchor values in the remapped codeword.

Abstract: A codeword is generated from a message. One or more anchor values are appended to the codeword at predetermined anchor positions. Before the codeword is stored in a memory block, the locations and values of stuck cells in the memory block are determined. Based on the values and positions of the stuck cells, the values of the codeword are remapped so that values of the codeword that are the same as the values of the stuck cells are placed at the positions of the stuck cells. The remapped codeword is stored in the memory block. When the message is later read, the original codeword can be recovered from the remapped codeword based on the locations of the anchor values in the remapped codeword.

Abstract: A codeword is generated from a message. One or more anchor values are appended to the codeword at predetermined anchor positions. Before the codeword is stored in a memory block, the locations and values of stuck cells in the memory block are determined. Based on the values and positions of the stuck cells, the values of the codeword are remapped so that values of the codeword that are the same as the values of the stuck cells are placed at the positions of the stuck cells. The remapped codeword is stored in the memory block. When the message is later read, the original codeword can be recovered from the remapped codeword based on the locations of the anchor values in the remapped codeword.

Abstract: Cloud data storage systems, methods, and techniques partition system data symbols into predefined-sized groups and then encode each group to form corresponding parity symbols, encode all data symbols into global redundant symbols, and store each symbol (data, parity, and redundant) in different failure domains in a manner that ensures independence of failures. In several implementations, the resultant cloud-encoded data features both data locality and ability to recover up to a predefined threshold tolerance of simultaneous erasures (unavailable data symbols) without any information loss. In addition, certain implementations also feature the placement of cloud-encoded data in domains (nodes or node groups) to provide similar locality and redundancy features simultaneous with the recovery of an entire domain of data that is unavailable due to software or hardware upgrades or failures.

Abstract: A generator matrix is provided to generate codewords from messages of write operations. Rather than generate a codeword using the entire generator matrix, some number of bits of the codeword are determined to be, or designated as, stuck bits. One or more submatrices of the generator matrix are determined based on the columns of the generator matrix that correspond to the stuck bits. The submatrices are used to generate the codeword from the message, and only the bits of the codeword that are not the stuck bits are written to a memory block. By designating one or more bits as stuck bits, the operating life of the bits is increased. Some of the submatrices of the generator matrix may be pre-computed for different stuck bit combinations. The pre-computed submatrices may be used to generate the codewords, thereby increasing the performance of write operations.

Abstract: A codeword is generated from a message. One or more anchor values are appended to the codeword at predetermined anchor positions. Before the codeword is stored in a memory block, the locations and values of stuck cells in the memory block are determined. Based on the values and positions of the stuck cells, the values of the codeword are remapped so that values of the codeword that are the same as the values of the stuck cells are placed at the positions of the stuck cells. The remapped codeword is stored in the memory block. When the message is later read, the original codeword can be recovered from the remapped codeword based on the locations of the anchor values in the remapped codeword.

Abstract: A generator matrix is provided to generate codewords from messages of write operations. Rather than generate a codeword using the entire generator matrix, some number of bits of the codeword are determined to be, or designated as, stuck bits. One or more submatrices of the generator matrix are determined based on the columns of the generator matrix that correspond to the stuck bits. The submatrices are used to generate the codeword from the message, and only the bits of the codeword that are not the stuck bits are written to a memory block. By designating one or more bits as stuck bits, the operating life of the bits is increased. Some of the submatrices of the generator matrix may be pre-computed for different stuck bit combinations. The pre-computed submatrices may be used to generate the codewords, thereby increasing the performance of write operations.

Abstract: Cloud data storage systems, methods, and techniques partition system data symbols into predefined-sized groups and then encode each group to form corresponding parity symbols, encode all data symbols into global redundant symbols, and store each symbol (data, parity, and redundant) in different failure domains in a manner that ensures independence of failures. In several implementations, the resultant cloud-encoded data features both data locality and ability to recover up to a predefined threshold tolerance of simultaneous erasures (unavailable data symbols) without any information loss. In addition, certain implementations also feature the placement of cloud-encoded data in domains (nodes or node groups) to provide similar locality and redundancy features simultaneous with the recovery of an entire domain of data that is unavailable due to software or hardware upgrades or failures.

Abstract: Disclosed is a method of scanning a data stream in a single pass to obtain uniform data samples from selected intervals. The method comprises randomly selecting elements from the stream for storage in one or more data buckets and, then, randomly selecting multiple samples from the bucket(s). Each sample is associated with a specified interval immediately prior to a selected point in time. There is a balance of probabilities between the selection of elements stored in the bucket and the selection of elements included in the samples so that elements scanned during the specified interval are included in the sample with equal probability. Samples can then be used to estimate the degree of sortedness of the stream, based on counting how many elements in the sequence are the rightmost point of an interval such that majority of the interval's elements are inverted with respect to the interval's rightmost element.

Abstract: Disclosed is a method of scanning a data stream in a single pass to obtain uniform data samples from selected intervals. The method comprises randomly selecting elements from the stream for storage in one or more data buckets and, then, randomly selecting multiple samples from the bucket(s). Each sample is associated with a specified interval immediately prior to a selected point in time. There is a balance of probabilities between the selection of elements stored in the bucket and the selection of elements included in the samples so that elements scanned during the specified interval are included in the sample with equal probability. Samples can then be used to estimate the degree of sortedness of the stream, based on counting how many elements in the sequence are the rightmost point of an interval such that majority of the interval's elements are inverted with respect to the interval's rightmost element.