Maximum distance separable (MDS) codes have the optimal trade-off between storage efficiency and fault tolerance, which are widely used in distributed storage systems. As typical non-MDS codes, simple regenerating codes (SRCs) can achieve both smaller repair bandwidth and smaller repair locality than traditional MDS codes in repairing single-node erasure. In this paper, we propose {\em generalized simple regenerating codes} (GSRCs) that can support much more parameters than that of SRCs. We show that there is a trade-off between sub-packetization and fault tolerance in our GSRCs, and SRCs achieve a special point of the trade-off of GSRCs. We show that the fault tolerance of our GSRCs increases when the sub-packetization increases linearly. We also show that our GSRCs can locally repair any singe-symbol erasure and any single-node erasure, and the repair bandwidth of our GSRCs is smaller than that of the existing related codes.

翻译：最大距离可分（MDS）码在存储效率与容错能力之间具有最优的权衡，广泛应用于分布式存储系统。作为典型的非MDS码，简单再生码（SRCs）在修复单节点擦除时，能够比传统MDS码实现更小的修复带宽和更小的修复局部性。本文提出广义简单再生码（GSRCs），可支持比SRCs更丰富的参数。我们证明GSRCs中子分组与容错能力之间存在权衡关系，而SRCs恰好达到该权衡的一个特殊点。研究表明，随着子分组线性增加，GSRCs的容错能力相应提升。此外，GSRCs可本地修复任意单符号擦除和任意单节点擦除，其修复带宽小于现有相关编码方案。