A Vertical-Horizontal Framework for Building Rack-Aware Regenerating Codes

Rack-aware regenerating codes (RRCs) achieve the optimal repair bandwidth for single node failures in the hierarchical data center where nodes are organized into racks and the intra-rack communication is cost-free. In this work, a vertical-horizontal framework is proposed for building RRCs from MDS array codes and regenerating codes (RCs). Particularly for RRCs with the minimum storage (i.e., MSRR codes), the framework is further improved to achieve lower sub-packetization. As a key for building MSRR codes, MSR codes (i.e., RCs with the minimum storage) with improved sub-packetization level are also developed. Applying the newly derived MSR codes into the vertical-horizontal framework, MSRR codes with an improved sub-packetization level are explicitly constructed, and those achieving the lowest sub-packetization by far are proved to exist over sufficiently large fields.