On Some Capacity-Achieving Fractional Repetition Codes

Abstract

Modern vehicle-based distributed storage networks need to provide efficient data recovery services due to the high mobility nature of storage vehicles. Compared with the simple replication scheme, erasure codes have been increasingly deployed in practical systems to achieve better storage performance. Specifically, fractional repetition (FR) codes are a class of repair efficient erasure codes characterized by the features of uncoded exact repair and minimum repair bandwidth. In this paper, we consider the capacity of FR codes, which is the maximum amount of information that can be obtained by any user contacting <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> out of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> storage nodes in the code based system. We present several families of FR codes that achieve a tight upper bound on the FR capacity, which are derived from combinatorial designs. The proposed constructions extend the parameter values of capacity-achieving FR codes to larger sets, and the resulting codes are of practical interest for vehicle-based distributed storage systems.