Lower Bounds on Bandwidth Requirements of Regenerating Code Parameter Scaling in Distributed Storage Systems

In a fault-tolerant Distributed Storage System (DSS) that depends on regenerating codes, there may be a variety of motivations for the system or the user to switch from one set of code parameters (<inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula>) to another. For example, the user may change their demand on reliability or the system may want to change the configuration due to implementation challenges, cost considerations and issues related to availability/ accessibility of geographically-distributed nodes. This can be managed by a well-designed DSS capable of dynamically scaling the parameters. In this letter, we present lower bounds on the bandwidth requirements for moving from a regenerating code configuration to another. In case of functional repair, our lower bounds are achievable, which helps the system designers identify the minimum-cost scaling strategy.