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Title:On error correcting codes for distributed storage
Author(s):Li, Xiao
Director of Research:Duursma, Iwan
Doctoral Committee Chair(s):Reznick, Bruce
Doctoral Committee Member(s):Yong, Alexander; Milenkovic, Olgica
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Coding Theory, Distributed Storage
Abstract:Two popular directions of error correcting codes for distributed storage are codes with additional recovery or regenerating properties. First we have codes for additional recovery properties. Codewords in array format find applications in disk storage where columns are stored on different disks in combination with parity checks across disks that protect data against disk failures. The addition of global parities protects against sector failures on any of the disks while keeping storage overhead low. We construct sector-disk array codes that tolerate any combination of two disk failures and three sector failures with minimal overhead. This constructs for the first time codes with these parameters without relying on exhaustive search. In the regenerating direction we have some modified layered codes in a two stage construction that gives regenerating codes with small field size. For more general parameters we define a Johnson graph code as a subspace of labelings of the vertices in a Johnson graph with the property that labelings are uniquely determined by their restriction to vertex neighborhoods specified by the parameters of the code. We give a construction and main properties for the codes. We show their role in the concatenation of layered codes to give regenerating codes for storage systems. Focusing on the Minimum Storage regenerating (MSR) point with $d=n-1$, we present graphical representations of codes with parameters \\ $((n,k,d), (\alpha, \beta)) = ((qt, q(t-1), qt-1),(q^t, q^{t-1}))$ over small field size.
Issue Date:2020-05-05
Type:Thesis
URI:http://hdl.handle.net/2142/107954
Rights Information:Copyright 2020 Xiao Li
Date Available in IDEALS:2020-08-26
Date Deposited:2020-05


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