Flexible Fractional Repetition Codes for Distributed Storage Networks
  Consider the following fundamental question of distributed storage networks: Given any arbitrary $(n,k,d)$ values, whether there exists an intelligent helper selection scheme (assuming unlimited memory and computing power) that can strictly improve the storage-bandwidth (S-B) tradeoff. Ahmad et al. 18' answered this question by proving that for a subset of $(n,k,d)$ values, no helper selection scheme can ever improve the S-B tradeoff, and for the $(n,k,d)$ not in that subset, a new scheme called family helper selection (FHS) can strictly improve the S-B tradeoff over a blind helper selection scheme. Nonetheless, the analysis of FHS is done by a min-cut analysis with no actual code construction.   This work fills this gap between pure min-cut analysis and actual code construction by pairing FHS with a new, generalized version of the existing fractional repetition (FR) codes. Specifically, existing FR codes are exact-repair codes that admit the highly-desirable repair-by-transfer property, but its unique construction limits the application to a restricted set of $(n,k,d)$ values. In contrast, our new construction, termed flexible fractional repetition codes, can be applied to arbitrary $(n,k,d)$ while retaining most of the practical benefits of FR codes, i.e., admitting small repair bandwidth, being exact-repair, and being almost repairable-by-transfer. 
Imad Ahmad and Chih-Chun Wang
cs.IT math.IT