Fractional Repetition and Erasure Batch Codes

TL;DR

This paper introduces fractional repetition batch (FRB) codes combining features of batch and fractional repetition codes for efficient data retrieval and repair in distributed storage systems, and proposes erasure combinatorial batch codes (ECBCs) for node failure tolerance.

Contribution

It presents the novel concept of FRB codes that enable both uncoded repairs and parallel data reads, and introduces ECBCs for enhanced node failure resilience.

Findings

FRB codes enable efficient uncoded repairs and parallel reads.

ECBCs provide node failure tolerance in batch coding.

Examples based on transversal designs and affine planes illustrate constructions.

Abstract

Batch codes are a family of codes that represent a distributed storage system (DSS) of $n$ nodes so that any batch of $t$ data symbols can be retrieved by reading at most one symbol from each node. Fractional repetition codes are a family of codes for DSS that enable efficient uncoded repairs of failed nodes. In this work these two families of codes are combined to obtain fractional repetition batch (FRB) codes which provide both uncoded repairs and parallel reads of subsets of stored symbols. In addition, new batch codes which can tolerate node failures are considered. This new family of batch codes is called erasure combinatorial batch codes (ECBCs). Some properties of FRB codes and ECBCs and examples of their constructions based on transversal designs and affine planes are presented.