Repair Schemes of Rack-Aware Reed-Solomon Codes: Providing A Tradeoff Between the Sub-Packetization Size and the Cross-Rack Repair Bandwidth

In practical data centers,  storage nodes are grouped and distributed in different racks, where the communication cost across racks is much more expensive than that within rack.  The concept of rack-aware maximum distance separable (MDS) codes has been put forward in recent literatures to deal with rack architecture. In this paper, the cross-rack repair bandwidth and sub-packetization size of rack-aware Reed-Solomon (RS) codes are studied. Cross-rack repair bandwidth is defined as the amount of information transmitted between the racks in the repair process of a failed node. RS codes can be regarded as polynomials over a finite field $GF(q^t)$ evaluated at a set of points, where $t$ is referred to as the sub-packetization size. Smaller cross-rack repair bandwidth decreases the network usage in data centers, and smaller sub-packetization size is conducive to the implementation of RS code with lower complexity. Previous RS codes that reach the rack-aware cut-set bound on cross-rack repair bandwidth either have sub-packetization size exponential in the code length or require strictly limited parameter conditions.

In this paper, the lower bound on the cross-rack repair bandwidth related to  sub-packetization size for rack-aware RS codes is given, which is asymptotically reachable under some parameters, and three repair schemes of rack-aware RS codes which provide a tradeoff between the sub-packetization size and the cross-rack repair bandwidth are shown.