Locality and Availability with Multiple Erasure Correction

摘要

Locally Recoverable Codes (LRC) that can correct one or more erasures in each local group exist. An LRC is said to have availability if each symbol has disjoint recovery sets and the symbol can be recovered from any of the disjoint sets. Tamo and Barg constructed optimal codes with availability, but different disjoint repair groups can have different locality for each information symbol. No bound on minimum Hamming distance exists for codes with availability in this scenario. Codes with availability can also locally correct multiple erasures in a local group. But the disk I/O is higher. We construct codes with different locality for different disjoint repair groups for each information symbol and derive a bound on the minimum hamming distance of these codes. We show that different disjoint repair groups can be protected by local codes of different minimum hamming distances. We show that optimal codes can be constructed based on pyramid codes.