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Construction of Locally Repairable Array Codes with Optimal Repair Bandwidth under the Rack-Aware Storage Model

Yumeng Yang, Han Cai, Xiaohu Tang

TL;DR

This work addresses efficient repair in rack-aware distributed storage by extending locally repairable codes (LRCs) to a rack-based, array-code setting. It generalizes the Tamo-Barg framework using good polynomials to achieve $ (r,u-r+1) $-locality within each rack and combines with regenerating-code ideas to enable bandwidth-efficient repairs when multiple racks are affected. The paper provides (i) a generic construction yielding $(n=u\bar{n}, r\bar{k}; l)$ LRCs with $(r,u-r+1)$-locality, (ii) a detailed repair mechanism that achieves the rack-aware cut-set bound for cross-rack repairs, and (iii) an explicit bandwidth-optimal family inspired by MSR codes, enabling optimal repair of a single overloaded rack. This work broadens the applicability of rack-aware codes by enabling diverse erasure patterns with low cross-rack bandwidth, which is crucial for scalable, fault-tolerant distributed storage systems.

Abstract

In this paper, we discuss codes for distributed storage systems with hierarchical repair properties. Specifically, we devote attention to the repair problem of the rack-aware storage model with locality, aiming to enhance the system's ability to repair a small number of erasures within each rack by locality and efficiently handling a rack erasure with a small repair bandwidth. By employing the regenerating coding technique, we construct a family of array codes with $(r,u-r+1)$-locality, where the $u$ nodes of each repair set are systematically organized into a rack. When the number of failures is less than $u - r + 1$, these failures can be repaired without counting the system bandwidth. In cases where the number of failures exceeds the locality, the failed nodes within a single rack can be recovered with optimal cross-rack bandwidth.

Construction of Locally Repairable Array Codes with Optimal Repair Bandwidth under the Rack-Aware Storage Model

TL;DR

This work addresses efficient repair in rack-aware distributed storage by extending locally repairable codes (LRCs) to a rack-based, array-code setting. It generalizes the Tamo-Barg framework using good polynomials to achieve -locality within each rack and combines with regenerating-code ideas to enable bandwidth-efficient repairs when multiple racks are affected. The paper provides (i) a generic construction yielding LRCs with -locality, (ii) a detailed repair mechanism that achieves the rack-aware cut-set bound for cross-rack repairs, and (iii) an explicit bandwidth-optimal family inspired by MSR codes, enabling optimal repair of a single overloaded rack. This work broadens the applicability of rack-aware codes by enabling diverse erasure patterns with low cross-rack bandwidth, which is crucial for scalable, fault-tolerant distributed storage systems.

Abstract

In this paper, we discuss codes for distributed storage systems with hierarchical repair properties. Specifically, we devote attention to the repair problem of the rack-aware storage model with locality, aiming to enhance the system's ability to repair a small number of erasures within each rack by locality and efficiently handling a rack erasure with a small repair bandwidth. By employing the regenerating coding technique, we construct a family of array codes with -locality, where the nodes of each repair set are systematically organized into a rack. When the number of failures is less than , these failures can be repaired without counting the system bandwidth. In cases where the number of failures exceeds the locality, the failed nodes within a single rack can be recovered with optimal cross-rack bandwidth.
Paper Structure (7 sections, 6 theorems, 21 equations, 3 figures)

This paper contains 7 sections, 6 theorems, 21 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. System Models
  4. Repair Scheme for Rack-Aware Locally Repairable Codes
  5. A Generic Construction
  6. Repair Mechanism
  7. A Family of Bandwidth-Optimal Locally Repairable Array Codes

Key Result

Theorem 1

Let $\mathcal{C}$ be a $(u\bar{n},u\bar{k};l)$ locally repairable array code with $(r,\delta=u-r+1)$-locality, where $u$ be the size of the local repair group. Denote by ${\epsilon}_i$ the number of failures in $i$-th group. For any $i\in[\bar{n}]$, ${\epsilon}_{i} \in [u]$ and any subset $D\subsete

Figures (3)

  • Figure 1: Homogeneous Storage Model
  • Figure 2: Rack-Aware Storage Model
  • Figure 3: Rack-Aware System with Locality

Theorems & Definitions (13)

  • Definition 1: Locally Repairable Array Code, gopalan2012localityprakash2012optimal
  • Definition 2: Generalized Reed-Solomon Code, MS77
  • Definition 3: Dual Code, MS77
  • Theorem 1: CMS+23
  • Definition 4: Good Polynomial TB14
  • Lemma 1: Chinese Remainder Theorem, MS77
  • Lemma 2: CMS+23
  • Theorem 2
  • proof
  • Theorem 3
  • ...and 3 more