In distributed storage, cooperative repair is to simultaneously recover h (h >1) node erasures by downloading data from surviving nodes as well as collaboration between the h replacement nodes. In this work, we propose a generalized cooperative repair framework for Reed-Solomon (RS) codes with two erasures. The key idea is to construct parity-check polynomials for the two replacement nodes respectively and then reduce the repair problem to the design of a linearized permutation polynomial related to the parity-check polynomials. We provide constructions of the linearized permutation polynomial in several cases, leading to cooperative repair schemes accordingly. Compared with the schemes given by Dau et al. 2021, our schemes retain the same repair bandwidth while apply to a much wider parameter regime and need only one-round collaboration. Finally we further reduce the repair bandwidth by the lifting method for RS codes of short length.

Publication:

IEEE Transactions on Information Theory (Volume: 70, Issue: 7, July 2024)

http://dx.doi.org/10.1109/TIT.2023.3347654

Author:

Jingke Xu

School of Information Science and Engineering, Shandong Agricultural University, Tai’an 271018, China

Email: xujingke@sdau.edu.cn

Yaqian Zhang

School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Email: zhangyq9@sjtu.edu.cn

Ke Wang

KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China, and also with the School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049

China

Email: wangke195@mails.ucas.ac.cn

Zhifang Zhang

KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China, and also with the School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049

China

Email: zfz@amss.ac.cn