2 research outputs found
Lower bounds for total storage of multiset combinatorial batch codes using linear programming
The class of multiset combinatorial batch codes (MCBCs) was introduced by Zhang et al. (2018) as a generalization of combinatorial batch codes (CBCs). MCBCs allow multiple users to retrieve items in parallel in a distributed storage system and a fundamental objective in this study is to determine the minimum total storage given certain requirements.We formulate an integer linear programming problem so that its optimal solution provides a lower bound of the total storage of MCBCs. Borrowing techniques from linear programming, we improve known lower bounds in some cases and also, determine the exact values for some parameters.Info-communications Media Development Authority (IMDA)National Research Foundation (NRF)Accepted versionThe authors would like to express their gratitude to the Associate Editor and the two anonymous reviewers for their constructive comments and suggestions which significantly improve the presentation of this work. This research of Han Mao Kiah is supported by the National Research Foundation, Singapore under its Strategic Capability Research Centres Funding Initiative. H. Zhang is supported by Singapore National Research Foundation grant NRF-RSS2016-004
Bounds and Constructions for Generalized Batch Codes
Private information retrieval (PIR) codes and batch codes are two important
types of codes that are designed for coded distributed storage systems and
private information retrieval protocols. These codes have been the focus of
much attention in recent years, as they enable efficient and secure storage and
retrieval of data in distributed systems.
In this paper, we introduce a new class of codes called \emph{-batch
codes}. These codes are a type of storage codes that can handle any multi-set
of requests, comprised of distinct information symbols. Importantly,
PIR codes and batch codes are special cases of -batch codes.
The main goal of this paper is to explore the relationship between the number
of redundancy symbols and the -batch code property. Specifically, we
establish a lower bound on the number of redundancy symbols required and
present several constructions of -batch codes. Furthermore, we extend
this property to the case where each request is a linear combination of
information symbols, which we refer to as \emph{functional -batch
codes}. Specifically, we demonstrate that simplex codes are asymptotically
optimal functional -batch codes, in terms of the number of redundancy
symbols required, under certain parameter regime.Comment: 25 page