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

<p>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.</p> <p><br></p> <p>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.</p> <p><br></p>