On the interior points of the storage-repair bandwidth tradeoff of regenerating codes

Abstract

It is well known that it is possible to construct regenerating codes with exact repair that operate at the minimum storage regeneration (MSR) and minimum bandwidth regenerating (MBR) endpoints of the storage-repair bandwidth tradeoff. It has also been known for some time, that it is not possible to construct exact-repair codes that operate exactly at an interior point, except possibly, in a small region adjacent to the MSR point. There have been three recent results relating to code constructions for the interior points. In the first, a normalized version of the classical storage-repair bandwidth tradeoff is introduced. This shows that when measured against practical metrics such as storage overhead and average repair bandwidth per unit time and unit data symbol stored, interior-point constructions are of equal importance as constructions for MSR and MBR points. A second major result uses an information-theory inequality prover to establish that it is not possible in general, to construct codes that achieve the interior points even asymptotically. The third result presents a construction for regenerating codes that does better than space-sharing, compares well with codes for MSR and MBR points when viewed in the normalized tradeoff framework, and which is capable of achieving a single interior point. An overview of these results is presented here.