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Robust Dynamic Coded Distributed Storage with Partially Storage Constrained Servers

Chen Zhao, Haobo Jia, Zhuqing Jia

TL;DR

The paper tackles Robust Dynamic Coded Distributed Storage with partially storage constrained servers, addressing read robustness to dropouts and secure updates under mixed storage constraints. It introduces tight converse bounds on the update threshold and the read/write communication costs, and then provides a constructive achievability using staircase codes with a novel re-encoding step to cope with partial storage limits. The results yield a complete characterization of fundamental limits, including exact update thresholds and cost bounds, and show how a heterogeneous storage setting can reduce to and extend the homogeneous case. The work advances the theory of robust, privacy-preserving distributed storage and has potential implications for practical systems with mixed storage capabilities and dynamic operation constraints.

Abstract

We consider the problem of Robust Dynamic Coded Distributed Storage (RDCDS) with partially storage constrained servers where the goal is to enable robust (resilient to server dropouts) and efficient (as measured by the communication costs) read and update operations, subject to the constraint that the storage at $S$ out of $N$ servers is limited by $1/K_c$ the size of the message. Building upon previously established converse arguments and achievability schemes by Jia et al., in this work we develop a set of new converse arguments and coding designs that enable us to completely characterize the fundamental limits of RDCDS with partially storage constrained servers, i.e., the minimum number of available servers for feasible update operation and the minimum communication costs for read and update operations across various server dropout scenarios.

Robust Dynamic Coded Distributed Storage with Partially Storage Constrained Servers

TL;DR

The paper tackles Robust Dynamic Coded Distributed Storage with partially storage constrained servers, addressing read robustness to dropouts and secure updates under mixed storage constraints. It introduces tight converse bounds on the update threshold and the read/write communication costs, and then provides a constructive achievability using staircase codes with a novel re-encoding step to cope with partial storage limits. The results yield a complete characterization of fundamental limits, including exact update thresholds and cost bounds, and show how a heterogeneous storage setting can reduce to and extend the homogeneous case. The work advances the theory of robust, privacy-preserving distributed storage and has potential implications for practical systems with mixed storage capabilities and dynamic operation constraints.

Abstract

We consider the problem of Robust Dynamic Coded Distributed Storage (RDCDS) with partially storage constrained servers where the goal is to enable robust (resilient to server dropouts) and efficient (as measured by the communication costs) read and update operations, subject to the constraint that the storage at out of servers is limited by the size of the message. Building upon previously established converse arguments and achievability schemes by Jia et al., in this work we develop a set of new converse arguments and coding designs that enable us to completely characterize the fundamental limits of RDCDS with partially storage constrained servers, i.e., the minimum number of available servers for feasible update operation and the minimum communication costs for read and update operations across various server dropout scenarios.

Paper Structure

This paper contains 18 sections, 4 theorems, 63 equations, 2 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Main Results
  4. Converse Proof of Theorem \ref{['thm:main']}
  5. Achievability Proof of Theorem \ref{['thm:main']}
  6. Motivating Example
  7. Construction of the Storage
  8. Execution of the Read Operation
  9. Execution of the Update Operation
  10. General Scheme
  11. Construction of the Storage
  12. Execution of the Read Operation
  13. When $|\mathcal{D}^{(t)}|\leq N-\Omega-K_c$
  14. When $|\mathcal{D}^{(t)}|> N-\Omega-K_c$
  15. Execution of the Update Operation
  16. ...and 3 more sections

Key Result

Theorem 1

At time slot $t>t_0$, we have where $\mathcal{D}$ is the set of $N$-dimensional vectors $(D_1, \cdots, D_N)\in\mathbb{R}_+^N$ such that and $\mathcal{U}$ is the set of $N$-dimensional vectors $(U_1, \cdots, U_N)\in\mathbb{R}_+^N$ such that And our scheme achieves the above bounds simultaneously at any time slot $t\in\mathbb{N}$.

Figures (2)

  • Figure 1: The problem of robust dynamic coded distributed storage with partially storage constrained servers. The servers marked with light orange have storage limits; the others have no explicit storage limit.
  • Figure 2: The illustration of the realization of the corresponding sets in the proof of the lower bound on the update threshold $R_u^{(t)}$.

Theorems & Definitions (6)

  • Theorem 1
  • Remark 1
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • proof