Recovery Algorithms for Linear Batch Codes

TL;DR

This paper systematically investigates linear batch codes and their recovery algorithms, exploring their hierarchy, generalizations, and graph-based methods to enhance understanding and application.

Contribution

It introduces and analyzes various recovery algorithms for linear batch codes, including new types and hierarchical structures, expanding the theoretical framework.

Findings

Graph-based batch codes are generalized to arbitrary bipartite graphs.

Hierarchy of recovery algorithms for linear batch codes is established.

New types of recovery algorithms are introduced and analyzed.

Abstract

Various types of recovery algorithms for batch codes have been investigated, such as asynchronous recovery or recovery as afforded by batch codes obtained from Almost Affinely Disjoint (AAD) families. In this paper, we offer the first systematic investigation of linear batch codes equipped with particular recovery algorithms. We introduce and investigate various known and new types of algorithms, and we investigate the order hierarchy of these types of batch codes. The simplest known recovery algorithms are those associated with graph-based batch codes. We investigate the resulting batch codes for arbitrary bipartite graphs, thereby generalizing some known results.