Nonlinear Repair of Reed-Solomon Codes

Roni Con*, Itzhak Tamo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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

Original languageEnglish
Pages (from-to)5165-5177
Number of pages13
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - 1 Aug 2022


FundersFunder number
Horizon 2020 Framework Programme852953


    • Reed-solomon codes
    • cut-set bound
    • repair bandwidth


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