On the Minimum Length of Functional Batch Codes with Small Recovery Sets
🤖 AI Summary
This study addresses the problem of minimizing the length of functional batch codes that support linear combination queries and enable recovery of each query from only a small number of encoded symbols. By generalizing classical batch codes to the setting of linear functions and incorporating constraints on small recovery sets, the work presents the first systematic analysis of upper and lower bounds on code length for this class of codes. Leveraging tools from algebraic coding theory, linear algebra, and numerical optimization, the authors derive novel theoretical bounds and validate their tightness and effectiveness through numerical experiments. This research provides both a theoretical foundation and practical guidance for designing efficient coding schemes in distributed storage systems that must support linear queries with minimal access overhead.
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
functional batch codes
minimum length
small recovery sets
distributed storage
linear codes
Innovation
Methods, ideas, or system contributions that make the work stand out.
functional batch codes
minimum length
small recovery sets
linear codes
distributed storage
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