General Sub-packetized Access-Optimal Regenerating Codes

This paper presents a novel construction of $(n,k,d=n-1)$ access-optimal regenerating codes for an arbitrary sub-packetization level $\alpha$ for exact repair of any systematic node. We refer to these codes as general sub-packetized because we provide an algorithm for constructing codes for any $\alpha$ less than or equal to $r^{\lceil \frac{k}{r} \rceil}$ where $\frac{k}{r}$ is not necessarily an integer. This leads to a flexible construction of codes for different code rates compared to existing approaches. We derive the lower and the upper bound of the repair bandwidth. The repair bandwidth depends on the code parameters and $\alpha$. The repair process of a failed systematic node is linear and highly parallelized, which means that a set of $\lceil \frac{\alpha}{r} \rceil$ symbols is independently repaired first and used along with the accessed data from other nodes to recover the remaining symbols.