Optimal Pliable Fractional Repetition Codes

Ahstract- The paper focuses on fractional repetition (FR) codes that are the key to constructing distributed storage codes with uncoded repair (i.e., a helper node reads the exact amount of data it needs to send to a replacement node and forwards it without any processing). Pliable FR codes are a new type of FR codes with the property that the per-node storage and repetition degree can easily be adjusted simultaneously, and are of vital importance for distributed storage systems where the parameters can dynamically change over time. A major drawback of existing pliable FR codes is that the supported file size is not large enough to meet a Singleton-like bound with equality when the number of storage nodes required to reconstruct the original file is large. To address this problem, this paper presents some general results on FR codes, including the exact file size of FR codes and sufficient conditions for FR codes to be optimal with respect to a Singleton-like bound. Based on bipartite graphs with arbitrary large girth, this paper also proposes a class of optimal pliable FR codes that attains a Singleton-like bound with equality. Examples are also provided to illustrate the proposed optimal pliable FR codes.