On the Average Locality of Locally Repairable Codes

Abstract

A linear block code with dimension k, length n, and minimum distance d is called a locally repairable code (LRC) with locality r if it can retrieve any coded symbol by at most r other coded symbols. LRCs have been recently proposed and used in practice in distributed storage systems (DSSs) such as Windows Azure storage and Facebook HDFS-RAID. Theoretical bounds on the maximum locality of LRCs (r) have been established. The average locality of an LRC (r) directly affects the costly repair bandwidth, disk I/O, and number of nodes involved in the repair process of a missing data block. There is a gap in the literature studying r. In this paper, we establish a lower bound on r of arbitrary (n, k, d) LRCs. Furthermore, we obtain a tight lower bound on r for a practical case where the code rate (R = k n ) is greater than (1 − 1 √ n ) 2 . Finally, we design three classes of LRCs that achieve the obtained bounds on r. Comparing with the existing LRCs, our proposed codes improve the average locality without sacrificing such crucial parameters as the code rate or minimum distance.

Asymptotic Bounds on the Rate of Locally Repairable Codes

“…A related relevant problem is obtaining such a bound when the average is computed per coordinate, i.e., the average is taken over the whole list of the N i repair groups of C i ; thus, each of the distinct repair groups is counted a number of times which equals the number of coordinates that it covers (namely, its size). A counterpart of the bound (2) for this setting was presented in [24].…”

Overview of Binary Locally Repairable Codes for Distributed Storage Systems

“…In [43], the advantages of (n, k, d, r) = (15,10,4,6) BLRC are discussed and compared with (16,10,4,5) non-binary LRC, (14,10) RS code, and three-replication with four metrics including encoding complexity, repair complexity, mean time to data loss, and storage capacity. The authors of [43] further analyzed the advantages of BLRCs with a high Hamming distance and average locality [44,45]. In this section, we introduce bounds for BLRCs and various construction methods of BLRCs.…”

Big Data-Based Improved Data Acquisition and Storage System for Designing Industrial Data Platform

“…Both Sqoop and Flume are the main framework for data acquisition modules [23], [24]. The Sqoop is used for data interaction between Hadoop and relational database, and imports relational database data into Hadoop distributed file storage system (HDFS) [25], [26]. As a data acquisition framework, the Flume supports the development of various data senders in the log file system to acquire their data, which simply processes the data and then stores the processed data in HDFS, Hive, or turns it into a producer of Kafka.…”