Array Codes With Local Properties

Abstract

In general, array codes consist of m × n arrays and in many cases, the arrays satisfy parity constraints along lines of different slopes (generally with a toroidal topology). Such codes are useful for RAID type of architectures, since they allow to replace finite field operations by XORs. We present expansions to traditional array codes of this type, like Blaum-Roth (BR) and extended EVENODD codes, by adding parity on columns. This vertical parity allows for recovery of one or more symbols in a column locally, i.e., by using the remaining symbols in the column without invoking the rest of the array. Properties and applications of the new codes are discussed, in particular to Locally Recoverable (LRC) codes.

QLOC: Quorums With Local Reconstruction Codes

“…A rich body of work on locally repairable codes exist, starting from the early pioneering works on the topic [1], [6], [14], and it continues to be a topic of research on its own accord, e.g., there are recent works [15], [16] which consider repairability of codes with similar array structures as used in this work. In that context, the current work should be viewed complementary in nature, and as adding a new design dimension laying foundations for further future work, on the amenability of the structures of these other existing repairable codes, to be leveraged for developing quorum systems for consistency, and to be evaluated in terms of the kind of consistency, fault-tolerance and concurrency that can be achieved by the quorum systems for these other instances of code families.…”

“…Content may change prior to final publication. (30,16) code. On the left, if the data symbol u1,2 in position (1, 2) is unavailable, either the row parity in row 1 or the column parity in column 2 could be used for degraded reads.…”

“…We use the specific instance to also benchmark its properties and demonstrate its suitability in meeting practical requirements in terms of storage overhead, fault-tolerance, and cost of data recovery or degraded reads in presence of faults. Specifically, we choose a (30,16) code that was analyzed in Example 1. We show next how to instantiate such a code, starting from a (24, 16) base code.…”

A Generalization of Array Codes with Local Properties and Efficient Encoding/Decoding

“…In addition to a column failure (i.e., all m symbols are failed in the failure column), another failure pattern is that one symbol of a column is failed. Recently, Expanded-Blaum-Roth (EBR) [2], [16] codes and Expanded-Independent-Parity (EIP) codes [2] extend BR codes [12] and Independent-Parity codes [11], respectively, and propose to tolerate any r column failures and locally repair one failed symbol within any column (called local repair property) by adding some DRAFT parity symbols into each column. This improves the performance of repairing a failed symbol, as the repair can be locally done within a column, without the need of accessing the symbols in other columns.…”

“…Furthermore, we show that the proposed GEBR codes have both a larger minimum symbol distance and a larger recovery ability of erased lines for some parameters when compared to EBR codes. We show that EBR codes can recover any r erased lines of a slope for any parameter r, which was an open problem in [2].…”