Limitations on the Achievable Repair Bandwidth of Piggybacking Codes with Low Substriping

TL;DR

This paper analyzes the theoretical limits of piggybacking codes with low substriping, revealing fundamental constraints on their repair bandwidth and providing explicit optimal constructions for certain parameters.

Contribution

It adapts a repair scheme characterization to piggybacking codes, establishing separation from general codes and proving impossibility results, along with explicit optimal code constructions.

Findings

Separation between piggybacking and general erasure codes

Impossibility results for certain piggybacking code subcategories

Explicit optimal constructions for specific parameters

Abstract

The piggybacking framework for designing erasure codes for distributed storage has empirically proven to be very useful, and has been used to design codes with desirable properties, such as low repair bandwidth and complexity. However, the theoretical properties of this framework remain largely unexplored. We address this by adapting a general characterization of repair schemes (previously used for Reed Solomon codes) to analyze piggybacking codes with low substriping. With this characterization, we establish a separation between piggybacking and general erasure codes, and several impossibility results for subcategories of piggybacking codes; for certain parameters, we also present explicit, optimal constructions of piggybacking codes.