Repairing Schemes for Tamo-Barg Codes

In this paper, the repair problem for erasures beyond locality in locally repairable codes is explored under a practical system setting, where a rack-Aware storage system consists of racks, each containing a few parity checks. This is referred to as a rack-Aware system with locality. Two repair schemes are devised to reduce the repair bandwidth for Tamo-Barg codes under the rack-Aware model by setting each repair set as a rack. Additionally, a cut-set bound for locally repairable codes under the rack-Aware model with locality is introduced. Using this bound, the second repair scheme is proven to be optimal. Furthermore, the partial-repair problem is considered for locally repairable codes under the rack-Aware model with locality, and both repair schemes and bounds are introduced for this scenario.n this paper, the repair problem for erasures beyond locality in locally repairable codes is explored under a practical system setting, where a rack-Aware storage system consists of racks, each containing a few parity checks. This is referred to as a rack-Aware system with locality. Two repair schemes are devised to reduce the repair bandwidth for Tamo-Barg codes under the rack-Aware model by setting each repair set as a rack. Additionally, a cut-set bound for locally repairable codes under the rack-Aware model with locality is introduced. Using this bound, the second repair scheme is proven to be optimal. Furthermore, the partial-repair problem is considered for locally repairable codes under the rack-Aware model with locality, and both repair schemes and bounds are introduced for this scenario.