  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.
