New results on Erasure Combinatorial Batch Codes

TL;DR

This paper extends the theory of Erasure Combinatorial Batch Codes to the general case where servers can send multiple files, providing new bounds and solutions, including an optimal approach for retrieving consecutive files.

Contribution

It generalizes existing results for erasure combinatorial batch codes to cases with multiple downloads per server and introduces an optimal solution for consecutive file retrieval scenarios.

Findings

Extended bounds for general t ≥ 1 cases.

Provided an optimal solution for consecutive file retrieval.

Generalized Hall's theorem application.

Abstract

We investigate in this work the problem of Erasure Combinatorial Batch Codes, in which $n$ files are stored on $m$ servers so that every set of $n-r$ servers allows a client to retrieve at most $k$ distinct files by downloading at most $t$ files from each server. Previous studies have solved this problem for the special case of $t=1$ using Combinatorial Batch Codes. We tackle the general case $t \geq 1$ using a generalization of Hall's theorem. Additionally, we address a realistic scenario in which the retrieved files are consecutive according to some order and provide a simple and optimal solution for this case.