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On Coded Caching Systems with Offline Users, with and without Demand Privacy against Colluding Users

Yinbin Ma, Daniela Tuninetti

TL;DR

The paper addresses coded caching when some users may be offline during delivery (hotplug) and, in a privacy variant, when active users’ demands must remain private against colluding peers. It introduces three new MDS-based coded-placement schemes (HT1, HT2, HT3) to tolerate offline users, proving exact optimality in several regimes and a constant-gap bound otherwise. It also extends privacy-preserving approaches (privacy-keys PK and virtual-users VU) to the hotplug setting, yielding reduced subpacketization and improved loads in many memory regimes. Comprehensive numerical evaluations and illustrative examples demonstrate the gains over baseline schemes and establish tight or near-tight performance in both non-private and private settings, highlighting the practical impact of coded placement for dynamic user activity and privacy requirements.

Abstract

Coded caching is a technique that leverages locally cached contents at the end users to reduce the network's peak-time communication load. Coded caching has been shown to achieve significant performance gains compared to uncoded schemes and is thus considered a promising technique to boost performance in future networks by effectively trading off bandwidth for storage. The original coded caching model introduced by Maddah-Ali and Niesen does not consider the case where some users involved in the placement phase, may be offline during the delivery phase. If so, the delivery may not start or it may be wasteful to perform the delivery with fictitious demands for the offline users. In addition, the active users may require their demand to be kept private. This paper formally defines a coded caching system where some users are offline, and investigates the optimal performance with and without demand privacy against colluding users. For this novel coded caching model with offline users, achievable and converse bounds are proposed. These bounds are shown to meet under certain conditions, and otherwise to be to within a constant multiplicative gap of one another. In addition, the proposed achievable schemes have lower subpacketization and lower load compared to baseline schemes (that trivially extend known schemes so as to accommodate for privacy) in some memory regimes.

On Coded Caching Systems with Offline Users, with and without Demand Privacy against Colluding Users

TL;DR

The paper addresses coded caching when some users may be offline during delivery (hotplug) and, in a privacy variant, when active users’ demands must remain private against colluding peers. It introduces three new MDS-based coded-placement schemes (HT1, HT2, HT3) to tolerate offline users, proving exact optimality in several regimes and a constant-gap bound otherwise. It also extends privacy-preserving approaches (privacy-keys PK and virtual-users VU) to the hotplug setting, yielding reduced subpacketization and improved loads in many memory regimes. Comprehensive numerical evaluations and illustrative examples demonstrate the gains over baseline schemes and establish tight or near-tight performance in both non-private and private settings, highlighting the practical impact of coded placement for dynamic user activity and privacy requirements.

Abstract

Coded caching is a technique that leverages locally cached contents at the end users to reduce the network's peak-time communication load. Coded caching has been shown to achieve significant performance gains compared to uncoded schemes and is thus considered a promising technique to boost performance in future networks by effectively trading off bandwidth for storage. The original coded caching model introduced by Maddah-Ali and Niesen does not consider the case where some users involved in the placement phase, may be offline during the delivery phase. If so, the delivery may not start or it may be wasteful to perform the delivery with fictitious demands for the offline users. In addition, the active users may require their demand to be kept private. This paper formally defines a coded caching system where some users are offline, and investigates the optimal performance with and without demand privacy against colluding users. For this novel coded caching model with offline users, achievable and converse bounds are proposed. These bounds are shown to meet under certain conditions, and otherwise to be to within a constant multiplicative gap of one another. In addition, the proposed achievable schemes have lower subpacketization and lower load compared to baseline schemes (that trivially extend known schemes so as to accommodate for privacy) in some memory regimes.
Paper Structure (55 sections, 19 theorems, 123 equations, 7 figures)

This paper contains 55 sections, 19 theorems, 123 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Contributions
  3. Paper Outline
  4. Notation Convention
  5. Problem Formulation
  6. Problem Formulation: Hotplug Model without Privacy
  7. Problem Formulation: Hotplug Model with Demand Privacy Against Colluding Users
  8. Known Schemes for Classical Model and Extensions to Baseline Schemes for Hotplug Model
  9. The YMA Scheme for Classical Model without Privacy
  10. Baseline Scheme 1 for Hotplug without Privacy: Extension of YMA to Hotplug
  11. Baseline Scheme 2 for Hotplug without Privacy: Decentralized Placement
  12. The PK Scheme for Classical Model with Privacy
  13. Baseline Scheme 1 for Hotplug with Privacy: Extension of PK to Hotplug
  14. Baseline Schemes 2 and 3 for Hotplug with Privacy: Extension of VU to Hotplug
  15. Main Results for Hotplug without Privacy
  16. ...and 40 more sections

Key Result

Theorem 3.1

For a $({\mathsf K}, {\mathsf N})$ classical coded caching system without privacy, the lower convex envelope of the following points is achievable The YMA scheme is optimal under the constraint of uncoded placement yu2017exact; otherwise, it is optimal to within a factor of 2 yu2018characterizing.

Figures (7)

  • Figure 1: Memory-load tradeoffs for the hotplug system with ${\mathsf N}=2$ files, ${\magenta \mathsf A}=2$ active users, and ${\mathsf K}=3$ total users. The converse bound is achievable by HT schemes in \ref{['eq:performanceNEW1']} and \ref{['eq:performanceNEW2']} for any ${\mathsf K} \geq {\magenta \mathsf A}=2$ with ${\mathsf N}=2$, and the optimal performance does not depend on ${\mathsf K}$.
  • Figure 2: Memory-load tradeoffs for the hotplug system with ${\mathsf N}=3$ files, ${\magenta \mathsf A}=3$ active users, and ${\mathsf K}=4$ total users. The converse is achievable for any ${\mathsf K} \geq {\magenta \mathsf A}=3$ with ${\mathsf N}=3$, except for ${\mathsf M}\in(1/3,1)$ which is open even in the classical setting tian2018symmetry. The performance of our scheme does not depend on ${\mathsf K}$.
  • Figure 3: Memory-load tradeoffs for the hotplug model with privacy when $({\magenta \mathsf A},{\mathsf K},{\mathsf N}) = (3, 6, 3)$.
  • Figure 4: Memory-load tradeoffs for the hotplug system with $({\mathsf K}, {\mathsf N}) = (15, 20)$ and different values of ${\magenta \mathsf A}$.
  • Figure 5: Memory-load tradeoffs for the hotplug system for with $({\magenta \mathsf A}, {\mathsf N}) = (5, 20)$ and various values of ${\mathsf K}$.
  • ...and 2 more figures

Theorems & Definitions (31)

  • Theorem 3.1: YMA
  • Theorem 3.2: Extension of YMA to Hotplug
  • Theorem 3.3: Extension of decentralized scheme to hotplug
  • Theorem 3.4: PK
  • Theorem 3.5: Extension of PK to Hotplug
  • Theorem 3.6: Extensions to hotplug with VU idea
  • Remark 1
  • Theorem 4.1: New Scheme 1
  • Remark 2: Sketch of achievability for Theorem \ref{['thm:HT1']}
  • Remark 3: Optimality for Theorem \ref{['thm:HT1']} in the small memory regime
  • ...and 21 more