A Cascade Code Construction for (n, k, d) Distributed Storage Systems

A novel class of exact-repair regenerating codes is introduced for a distributed storage system with arbitrary parameters $(n,\ k,\ d)$. The proposed construction is based on the optimum determinant codes for $(n,\ k=d,\ d)$ systems. This construction yields an achievable trade-off between the storage and the repair bandwidth, consisting of $k$ corner points, which meets the optimum trade-off at the MBR and MSR points, and improves all the previously known bounds for interior points. The sub-packetization level of the proposed code only depends on $k$ and $d$, but not number of nodes $n$. Further, the required field size for the proposed code is $\Theta(n)$. We conjecture that the proposed codes can universally achieve the optimum trade-off.