On Sequential Locally Repairable Codes

On Sequential Locally Repairable Codes

We consider the locally repairable codes (LRC), aiming at sequential recovering multiple erasures. We define the (n, k, r, t)SLRC (Sequential Locally Repairable Codes) as an [n, k] linear code where any t(≤ t) erasures can be sequentially recovered, each one by r (2 ≤ r < k) other code symbols. Sequential recovering means that the erased symbols are recovered one by one, and an already recovere...

On Sequential Locally Repairable Codes - for NVMW 2018.dvi

On Sequential Locally Repairable Codes Revised by Guangyue.dvi

We consider the locally repairable codes (LRC), aiming at sequentially recovering multiple erasures; in particular, we propose and study the so-called (n, k, r, t)-SLRC (Sequential Locally Repairable Codes) as an [n, k] linear code where any t (≤ t) erasures can be sequentially recovered, each by r (2 ≤ r < k) other code symbols. Here, a sequential recovering means that the erased symbols are r...

Some Improvements on Locally Repairable Codes

The locally repairable codes (LRCs) were introduced to correct erasures efficiently in distributed storage systems. LRCs are extensively studied recently. In this paper, we first deal with the open case remained in [40] and derive an improved upper bound for the minimum distances of LRCs. We also give an explicit construction for LRCs attaining this bound. Secondly, we consider the construction...

List Decoding of Locally Repairable Codes

We show that locally repairable codes (LRCs) can be list decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error correction capabilities. The new decoding radius is derived and the asymptotic behavior is analyzed. We give a general list decoding algorithm for LRCs that achieves this radius along with an explicit realization for a class of LRCs ...