Fractional Repetition Codes With Flexible Repair From Combinatorial Designs

• Published in: IEEE transactions on information theory Vol. 62; no. 4; pp. 1565 - 1591
• Main Authors: Olmez, Oktay, Ramamoorthy, Aditya
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: affine geometry; Bandwidth; Bandwidths; Codes; combinatorial design; Combinatorics; Data storage systems; Decision support systems; Fractional repetition code; Geometry; high girth; Information theory; local repair; Maintenance engineering; Measurement; regenerating codes; Resilience; resolvable design; Steiner systems; local repair; affine geometry; Fractional repetition code; high girth; regenerating codes; Steiner systems; resolvable design; combinatorial design
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2016.2531720

Fractional repetition (FR) codes are a class of regenerating codes for distributed storage systems with an exact (table-based) repair process that is also uncoded, i.e., upon failure, a node is regenerated by simply downloading packets from the surviving nodes. In this paper, we present the constructions of FR codes based on Steiner systems and resolvable combinatorial designs, such as affine geometries, Hadamard designs, and mutually orthogonal Latin squares. The failure resilience of our codes can be varied in a simple manner. We construct codes with normalized repair bandwidth (β) strictly larger than one; these cannot be obtained trivially from codes with β = 1. Furthermore, we present the Kronecker product technique for generating new codes from existing ones and elaborate on their properties. FR codes with locality are those where the repair degree is smaller than the number of nodes contacted for reconstructing the stored file. For these codes, we establish a tradeoff between the local repair property and the failure resilience and construct codes that meet this tradeoff. Much of prior work only provided lower bounds on the FR code rate. In this paper, for most of our constructions, we determine the code rate for certain parameter ranges.