Example apparatus and methods monitor conditions in an object storage system. The conditions monitored may include a load balance measure in the system, a capacity balance measure in the system, a fault tolerance measure in the system, or a usage pattern measure in the system. A distribution plan or redistribution plan for storing or moving erasure codes in the object storage system may be determined based on the conditions. The distribution plan or the redistribution plan for the erasure codes may be updated dynamically in response to changing conditions in the object storage system. The distribution or redistribution may depend on a weighted combination of the load balance measure, the capacity balance measure, the fault tolerance measure, or the usage pattern measure so that responding to one sub-optimal condition (e.g., load imbalance) does not create a different sub-optimal condition (e.g., unacceptable fault tolerance).

Methods for data storage on polymers are provided. In various embodiments, an erasure error correcting code is selected. Input data is read from an input file. The erasure error correcting code is applied to the input data to generate a code word. The code word is encoded according to a chemical alphabet. A number of cycles required for synthesis is determined for the code word. The encoded code word is screened according to the number of cycles. The code word is retained where passing the screening.

An erasure code (EC)-based data processing method implemented by a storage controller includes obtaining K data chunks, dividing each of the K data chunks into two data slices, encoding the 2*K data slices based on a parity matrix including 2*M rows and 2*(K+M) columns of elements, to obtain 2*M parity slices, and separately storing the K data chunks and the M parity chunks in different storage devices.

Every time a node computer receives multidimensional data from a data source, the node computer which has received the multidimensional data in a computer system: writes the multidimensional data; reads the multidimensional data; analyzes the read multidimensional data; and outputs a result of the analysis. Such writing of the multidimensional data is data locality EC processing (Erasure Coding with data locality). The data locality EC processing is to: write all of one or more data chunks constituting the multidimensional data to the node computer; and write a parity of the data chunk, with respect to each of the one or more data chunks, to a node computer(s) other than the node computer.

An error correction circuit includes: a first error correction encoder for generating a plurality of row-codewords by performing first error correction encoding on each of a plurality of messages; a second error correction encoder for generating a plurality of column-codewords; a first error correction decoder for performing first error correction decoding on each of read row-vectors corresponding to the plurality of row-codewords, and outputting a soft information of the first error correction decoding; and a second error correction decoder for determining whether each of m-bit symbols in read column-vectors corresponding to the column-codewords is reliable, based on the soft information corresponding to each of the p-bit symbols, and performing second error correction decoding on the read column-vectors, based on the determination of whether each of the m-bit symbols is reliable.

According to various embodiments, there may be provided a method of encoding data, the method including providing a set of replica nodes, wherein each replica node of the set of replica nodes stores replica data identical to original data stored in a corresponding original node of a set of original nodes; receiving original data at each replica node of the set of replica nodes, wherein the received original data is transmitted from the corresponding original node of a different replica node; generating a first result at each replica node, based on the replica data stored therein and the received original data; and generating a second result at each replica node, based on the replica data stored therein and the first result from a different replica node; and replacing the replica data in each replica node with the second result from the respective replica node.

In order to reduce write tail latency, a storage system generates redundant write requests when performing a storage operation for an object. The storage operation is determined to be effectively complete when a minimum number of write requests have completed. For example, the storage system may generate twelve write requests and also generate four redundant write requests for a total of sixteen write requests. The storage system considers the object successfully stored once twelve of the sixteen writes complete successfully. To generate the redundant writes, the storage system may use replication or erasure coding. For replication, the storage system may issue a redundant write request for each of n chunks being written. For erasure coding, the storage system may use rateless codes which can generate unlimited number of parity chunks or use an n+k+k' erasure code which generates an additional k encoded chunks, in place of an n+k erasure code.

A quantum-state-refresh module of a memory system is configured to detect an error in an entangled qubit state stored therein by performing a redundant measurement of syndrome values corresponding to a quantum stabilizer code, with the redundant measurement being based on a block error-correction code. The quantum-state-refresh module includes a plurality of measurement sub-modules, each configured to measure a respective syndrome value or a respective parity value corresponding to the entangled qubit state. The total number of the measurement sub-modules is smaller than the codeword length of the block error-correction code, and the initial approximation of the punctured syndrome values is replaced in the decoding process by erasure values. With the block error-correction code appropriately constructed for the use of erasure values, the quantum-state-refresh module is advantageously capable of providing reliable error detection with fewer quantum gates than that used for the full-length measurement of the codeword.

Example apparatus and methods control whether and when hybrid rateless Reed Solomon (RS) error correcting codes (ECC) for a message are produced, stored, and distributed. The control may be based on a property (e.g., reliability, error state, speed) of a message recipient. Example apparatus and methods may also control whether and when fountain codes for the message are produced, stored, and distributed. Once again, the control may be based on a property of a message or ECC recipient. Both the hybrid rateless RS ECC and the fountain codes may be produced from data stored in a modified RS matrix. The modified RS matrix may store row-centric error detection codes (EDC) instead of conventional cyclic redundancy check (CRC) characters. The modified RS matrix may store column-centric ECC that may be produced serially. Different types or numbers of ECC may be produced, stored, and provided for different messages stored at different recipients.

A method of operating a storage system is provided. The method includes establishing a security context between a client and the storage system, the security context comprising a single ticket for multiple nodes within the storage system. The method includes distributing a first request to a first blade within the storage system and distributing a second request to a second blade within the storage system. The distributing the first request and the second request includes determining a node for handling the first request and the second request based on data within the single ticket.