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arXiv · 1305.2440

Rate Region of the (4,3,3) Exact-Repair Regenerating Codes

Chao Tian
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Abstract

Exact-repair regenerating codes are considered for the case (n,k,d)=(4,3,3), for which a complete characterization of the rate region is provided. This characterization answers in the affirmative the open question whether there exists a non-vanishing gap between the optimal bandwidth-storage tradeoff of the functional-repair regenerating codes (i.e., the cut-set bound) and that of the exact-repair regenerating codes. The converse proof relies on the existence of symmetric optimal solutions. For the achievability, only one non-trivial corner point of the rate region needs to be addressed, for which an explicit binary code construction is given.

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Chao Tian. 2013-05-10. Rate Region of the (4,3,3) Exact-Repair Regenerating Codes. https://arxiv.org/abs/1305.2440

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