On low repair complexity storage codes via group divisible designs

Fractional repetition (FR) codes are a family of storage codes that provide efficient node repair at the minimum bandwidth regenerating point. Specifically, the repair process is exact and uncoded, but table-based. Existing constructions of FR codes are primarily based on combinatorial designs such as Steiner systems, resolvable designs, etc. In this paper, we present a new explicit construction of FR codes, which adopts the theory of uniform group divisible designs, termed GDDFR codes. Our codes achieve the storage capacity of random access and are available for a wide range of parameters. In addition, our techniques allow for constructing FR codes with parameters that are not covered by Steiner systems, which answers an open question put forward in prior work.