Binary Locally Repairable Codes from Complete Multipartite Graphs

Abstract

This paper introduces a generalized notion, referred to as joint locality, of the usual locality in distributed storage systems and proposes a code construction of binary locally repairable codes with joint locality          . Joint locality is a set of numbers of nodes for repairing various failure patterns of nodes.The proposed scheme simplifies the code design problem utilizing complete multipartite graphs. Moreover, our construction can generate binary locally repairable codes achieving  -availability for any positive integer . It means that each node can be repaired by  disjoint repair sets of cardinality 2. This property is useful for distributed storage systems since it permits parallel access to hot data.

Binary Codes with Locality for Four Erasures

“…Alternate approaches for local recovery from multiple erasures can be found in [6], [12], [13], [14], [15], [16], [17], [18], [7], [19], [20], [21].…”

Binary codes with locality for multiple erasures having short block length

“…There is a second class of codes, termed as t-availability codes in which each code symbol is covered by t orthogonal parity checks, but these are only required to have support of size ≤ (r + 1) as opposed to the strict requirement of = (r + 1) discussed here. Codes with t-availability can be found discussed in [8], [9], [10], [11], [12], [13], [6], [14], [15], [16]. The sequential approach of recovering from multiple erasures, introduced in [17], can also be found discussed in [18], [19], [20].…”