On the Minimum Length of Functional Batch Codes with Small Recovery Sets
Provides theoretical bounds for a specialized coding problem in distributed storage, but the results are incremental and lack concrete performance numbers.
This work derives bounds on the minimum length of linear functional batch codes where each query is answered using a small number of coded symbols, and evaluates these bounds numerically.
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.