Abstract: An improved technique involves performing computations for partial stripe updates in a RAID at individual disk controllers rather than at the RAID controller. When a RAID controller receives a request to update old payload data at a block in a particular disk with update data, it sends the update data to the controller of that particular disk. The disk controller reads internally old data from the block, computes the difference between new and old data, replaces the old data on disk with the new data, and returns the difference to the RAID controller. The RAID controller computes difference values of the parity data from the difference values of the payload data received from the disk controllers. It then sends these difference values to the controllers of disks storing parity data. A controller of a disk storing parity data reads internally the corresponding data block, adds to it the difference value, and writes the result back to disk.

Abstract: An improved technique involves assigning a different generator matrix to each data stripe of the redundant disk array such that all of the different generator matrices represent the same code. For example, when a k×n generator matrix G represents a linear code C, k being the block length and n the code length, then for any invertible k×k matrix P, the matrix G?=PG is also a generator that represents C. When C is a systematic code, then G consists of a k×k identity matrix representing payload data concatenated with a k×(n?k) parity matrix representing parity data. Certain matrices P represent row operations on G, meaning that the matrix G? may have the columns of the identity matrix in G to different locations in G?.

Abstract: An improved technique applies polar codes to storage data to improve the reliability of a storage system that uses high-performance, solid-state disks as part of a RAID group for storing frequently-accessed data. Along these lines, a high-performance storage system having n solid-state disks assigns k of those disks as payload disks. The storage system partitions the payload data into a data vector that has k data symbols. The storage system then applies, to the k payload symbols, a (n, k) polar code generator matrix derived from k rows of the ? log2 n?-times Kronecker product of the matrix ? ( 1 0 1 1 ) to produce n encoded symbols and stores each of the encoded payload symbols in a solid-state disk of the RAID group.

Abstract: An improved technique involves assigning a different generator matrix to each data stripe of the redundant disk array such that all of the different generator matrices represent the same code. For example, when a k×n generator matrix G represents a linear code C, k being the block length and n the code length, then for any invertible k×k matrix P, the matrix G?=PG is also a generator that represents C. When C is a systematic code, then G consists of a k×k identity matrix representing payload data concatenated with a k×(n?k) parity matrix representing parity data. Certain matrices P represent row operations on G, meaning that the matrix G? may have the columns of the identity matrix in G to different locations in G?.

Abstract: A method is provided of encoding data within a RAID stripe, the RAID stripe being spread across k data disks and r redundancy disks of a RAID group, r?3, the RAID group having k+r disks, the k data disks and the r redundancy disks within the RAID stripe being distinct, such that, upon failure of any r disks of the k+r disks of the RAID group, the data can be fully recovered using the Forney algorithm. The method includes (a) partitioning the data into k data symbols, (b) storing each of the k data symbols to a respective data disk of the k data disks, (c) generating r Reed-Solomon redundancy symbols by applying the Forney algorithm to the k data symbols, and (d) storing each of the r Reed-Solomon redundancy symbols generated by the Forney algorithm to a respective redundancy disk of the r redundancy disks.

Abstract: An improved technique involves performing computations for partial stripe updates in a RAID at individual disk controllers rather than at the RAID controller. When a RAID controller receives a request to update old payload data at a block in a particular disk with update data, it sends the update data to the controller of that particular disk. The disk controller reads internally old data from the block, computes the difference between new and old data, replaces the old data on disk with the new data, and returns the difference to the RAID controller. The RAID controller computes difference values of the parity data from the difference values of the payload data received from the disk controllers. It then sends these difference values to the controllers of disks storing parity data. A controller of a disk storing parity data reads internally the corresponding data block, adds to it the difference value, and writes the result back to disk.

Abstract: An improved technique applies polar codes to storage data to improve the reliability of a storage system that uses high-performance, solid-state disks as part of a RAID group for storing frequently-accessed data. Along these lines, a high-performance storage system having n solid-state disks assigns k of those disks as payload disks. The storage system partitions the payload data into a data vector that has k data symbols. The storage system then applies, to the k payload symbols, a (n, k) polar code generator matrix derived from k rows of the ? log2 n?-times Kronecker product of the matrix ? ( 1 0 1 1 ) to produce n encoded symbols and stores each of the encoded payload symbols in a solid-state disk of the RAID group.

Abstract: A method is provided of encoding data within a RAID stripe, the RAID stripe being spread across k data disks and r redundancy disks of a RAID group, r?3, the RAID group having k+r disks, the k data disks and the r redundancy disks within the RAID stripe being distinct, such that, upon failure of any r disks of the k+r disks of the RAID group, the data can be fully recovered using the Forney algorithm. The method includes (a) partitioning the data into k data symbols, (b) storing each of the k data symbols to a respective data disk of the k data disks, (c) generating r Reed-Solomon redundancy symbols by applying the Forney algorithm to the k data symbols, and (d) storing each of the r Reed-Solomon redundancy symbols generated by the Forney algorithm to a respective redundancy disk of the r redundancy disks.