Abstract
Locally repairable codes (LRCs) have important applications in distributed storage systems. In this paper, we study q-ary [n, k, d] LRCs with (r, t, δ)-information-locality, where each of the i-th (1 ≤ i ≤ k) information symbol is contained in t punctured subcodes with length ≤ r + δ - 1, minimum distance δ, and the i-th information symbol is the unique common code symbol of these t subcodes, furthermore, each subcode contains exactly δ - 1 parity symbols. Firstly, an upper bound on the minimum distance of such q-ary LRCs with (r, t, δ)-information-locality is given. Then, we propose a general construction framework of q-ary optimal LRCs with (r, t, δ)-information-locality and minimum distanced = t(δ-1)+1, where the required field size is just q ≥ r+δ-2. The proposed optimal LRCs can always repair a failed information node locally in case of at most tδ - 1 node failures. Moreover, multiple repair subcodes can support parallel readings of data, thus make the proposed codes attractive for distributed storage systems with hot data.
Highlights
Modern large distributed storage systems usually store redundant data to ensure data reliability in case of storage node failures
Locally repairable codes (LRCs) [1] which can repair failed nodes efficiently have attracted a lot of interest
We study the bounds and constructions of [n, k, d] locally repairable codes (LRCs) with (r, t, δ)-information-locality where each local subcode contains exactly δ − 1 parity symbols
Summary
Modern large distributed storage systems usually store redundant data to ensure data reliability in case of storage node failures. A linear code is said to have (r, t, δ)-informationlocality if the i-th information symbol, for 1 ≤ i ≤ k, is contained in t punctured subcodes, each has length at most r +δ −1, minimum distance δ and their supports only intersect on the i-th coordinate, each local subcode contains exactly δ − 1 parity symbols. We study the bounds and constructions of [n, k, d] LRCs with (r, t, δ)-information-locality where each local subcode contains exactly δ − 1 parity symbols. The proposed codes can always repair a failed information node locally in case of at most tδ − 1 node failures, and these t repair subcodes of each information symbol can support parallel readings of data, which benefits storage systems with hot data.
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