On the Minimum Length of Functional Batch Codes with Small Recovery Sets

TL;DR

This paper investigates the minimum length of linear functional batch codes that allow small recovery sets, providing bounds and numerical evaluations to optimize distributed data storage and retrieval.

Contribution

It introduces bounds on the length of linear functional batch codes with small recovery sets, advancing understanding of their efficiency in data storage systems.

Findings

Derived bounds on code length for small recovery sets

Numerical evaluation of bounds and code parameters

Enhanced understanding of trade-offs in functional batch codes

Abstract

Batch codes are of potential use for load balancing and private information retrieval in distributed data storage systems. Recently, a special case of batch codes, termed functional batch codes, was proposed in the literature. In functional batch codes, users can query linear combinations of the information symbols, and not only the information symbols themselves, as is the case for standard batch codes. In this work, we consider linear functional batch codes with the additional property that every query is answered by using only a small number of coded symbols. We derive bounds on the minimum length of such codes, and evaluate the results by numerical computations.