Year: 2018
Type: article
Abstract: Locally recoverable (LRC) codes have recently been a focus point of research in coding theory due to their theoretical appeal and applications in distributed storage systems. In an LRC code, any erased symbol of a codeword can be recovered by accessing only a small number of other symbols. For LRC codes over a small alphabet (such as binary), the optimal rate-distance trade-off is unknown. We present several new combinatorial bounds on LRC codes including the locality-aware sphere packing and Plotkin bounds. We also develop an approach to linear programming (LP) bounds on LRC codes. The resulting LP bound gives better estimates in examples than the other upper bounds known in the literature. Further, we provide the tightest known upper bound on the rate of linear LRC codes with a given relative distance, an improvement over the previous best known bounds.
Authors: Abhishek Agarwal, Alexander Barg, Sihuang Hu, Arya Mazumdar, Itzhak Tamo
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: CCF-BSF: CIF: Small: Collaborative Research: Coding and Information - Theoretic Aspects of Local Data Recovery, CIF: Small: Collaborative Research: Efficient Codes and their Performance Limits for Distributed Storage Systems, G2759301425, G3413227351, CAREER: Reliability in Large-Scale Storage, G6439195795, CIF: Small: Collaborative Research: Combinatorial Joint Source-Channel Coding, G8246453351, CCF-BSF: CIF: Small: Collaborative Research: Coding and Information - Theoretic Aspects of Local Data Recovery
OpenAlex ID: W2963431689