  In this paper, we address the node repair problem of Reed-Solomon (RS) coded
distributed storage systems. Specifically, to overcome the challenges of
multiple-node failures of RS codes under the rack-aware storage model, we
employ good polynomials to guide the placement of the conventional RS codes
into racks and then propose a novel repair framework for the resultant
rack-aware RS codes, which can transform its repair to that under the
homogeneous storage model. As applications of our repair framework, firstly we
present the repair scheme of multiple-node failures for some existing
constructions, which only have non-trivial solutions for repairing a
single-node failure before. Secondly, we deduce several new constructions of
rack-aware RS codes supporting the repair of multiple-node failures within a
single rack and across multiple racks respectively.
