Outer bounds on the storage-repair bandwidth trade-off of exact-repair regenerating codes
by Birenjith Sasidharan; N. Prakash; M. Nikhil Krishnan; Myna Vajha; Kaushik Senthoor; P. Vijay Kumar
International Journal of Information and Coding Theory (IJICOT), Vol. 3, No. 4, 2016

Abstract: In this paper, three outer bounds on the normalised storage-repair bandwidth trade-off of regenerating codes having parameter set {(n, k, d), (α, β)} under the exact-repair (ER) setting are presented. The first outer bound, termed as the repair-matrix bound, is applicable for every parameter set (n, k, d), and in conjunction with a code construction known as improved layered codes, it characterises the normalised ER trade-off for the case (n, k = 3, d = n – 1). The bound shows that a non-vanishing gap exists between the ER and functional-repair (FR) trade-offs for every (n, k, d). The second bound, termed as the improved Mohajer-Tandon bound, is an improvement upon an existing bound due to Mohajer et al. and performs better in a region away from the minimum-storage-regenerating (MSR) point. However, in the vicinity of the MSR point, the repair-matrix bound outperforms the improved Mohajer-Tandon bound. The third bound is applicable to linear codes for the case k = d. In conjunction with the class of layered codes, the third outer bound characterises the normalised ER trade-off in the case of linear codes when k = d = n – 1.

Online publication date: Thu, 29-Sep-2016

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