Nonlinear Repair of Reed-Solomon Codes
نویسندگان
چکیده
The problem of repairing linear codes and, in particular, Reed Solomon (RS) has attracted a lot attention recent years due to their extreme importance distributed storage systems. In this problem, failed code symbol (node) needs be repaired by downloading as little information possible from subset the remaining nodes. By now, there are examples RS that have efficient repair schemes, and some even attain cut-set bound. However, these schemes fall short several aspects; they require considerable field extension degree. They do not provide any nontrivial scheme over prime fields. Lastly, all repairs, i.e., computed functions base field. Motivated question raised Guruswami Wootters, 2017, on power nonlinear we study codes. Our main results first with asymptotically optimal bandwidth (asymptotically matching bound). This is example also can outperform ones. show bound for tight fields proving tighter bound, using additive combinatorics ideas.
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2022
ISSN: ['0018-9448', '1557-9654']
DOI: https://doi.org/10.1109/tit.2022.3167615