2013/05/10 by Chao Tian, Tian, Chao · 3 citations
Computer Science · Mathematics · #Advanced Data Storage Technologies #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1305.2440
accepted, ISIT 2013, 5 pages
arxiv created 2013/05/10 · openalex publication_date 2013/05/10 · arxiv updated 2013/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.