BIROn - Birkbeck Institutional Research Online

Combinatorial batch codes

Stinson, D.R. and Wei, R. and Paterson, Maura B. (2009) Combinatorial batch codes. Advances in Mathematics of Communications 3 (1), pp. 13-27. ISSN 1930-5346.

[img]
Preview
Text (Pre-print (unrefereed))
2905.pdf

Download (429Kb) | Preview
Official URL: http://dx.doi.org/10.3934/amc.2009.3.13

Abstract

In this paper, we study batch codes, which were introduced by Ishai, Kushilevitz, Ostrovsky and Sahai in [4]. A batch code specifies a method to distribute a database of [n] items among [m] devices (servers) in such a way that any [k] items can be retrieved by reading at most [t] items from each of the servers. It is of interest to devise batch codes that minimize the total storage, denoted by [N] , over all [m] servers. We restrict out attention to batch codes in which every server stores a subset of the items. This is purely a combinatorial problem, so we call this kind of batch code a ''combinatorial batch code''. We only study the special case [t=1] , where, for various parameter situations, we are able to present batch codes that are optimal with respect to the storage requirement, [N] . We also study uniform codes, where every item is stored in precisely [c] of the [m] servers (such a code is said to have rate [1/c] ). Interesting new results are presented in the cases [c = 2, k-2] and [k-1] . In addition, we obtain improved existence results for arbitrary fixed [c] using the probabilistic method.

Item Type: Article
Keyword(s) / Subject(s): Batch codes, combinatorial set system
School or Research Centre: Birkbeck Schools and Research Centres > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
Depositing User: Administrator
Date Deposited: 08 Dec 2010 08:56
Last Modified: 06 Sep 2013 16:49
URI: http://eprints.bbk.ac.uk/id/eprint/2905

Archive Staff Only (login required)

Edit/View Item Edit/View Item