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Coded Caching for Combinatorial Multi-Access Hotplug Networks from $t$-Designs

Dhruv Pratap Singh, Anjana A. Mahesh, B. Sundar Rajan

TL;DR

This work extends coded caching to a hotplug, combinatorial multi-access setting where each user connects to an r-subset of C caches and only C' caches are online during delivery. It generalizes the HpPDA framework and introduces a t-design–based caching scheme that uses MDS-coded placement and a family of PDAs to manage heterogeneous online cache access, enabling decodability while eliminating redundant multicast transmissions. A key contribution is the characterization of achievable rate–memory trade-offs parameterized by a_{s,j} with decodability guaranteed when Y_j ≤ Y_{j-1}, and the demonstration that setting a_{s,j}=λ^t_s yields uniform access across active users; the framework also specializes to existing CRR schemes for r=1. Numerical results indicate the proposed t-design scheme outperforms certain hotplug benchmarks in specific memory regimes, illustrating practical gains from jointly optimizing hotplug and multi-access structures.

Abstract

We study hotplug coded caching in combinatorial multi-access networks, which generalizes existing hotplug coded caching models by allowing users to access multiple caches, while only a subset of caches is online during the delivery phase. We first generalize the Hotplug Placement Delivery Array (HpPDA) framework to the combinatorial multi-access setting. Based on this generalized framework, we propose a t-design-based coded caching scheme for combinatorial multi-access networks. We characterize a class of design parameters under which every active user has access to a sufficient number of coded subfiles to decode its requested file, and show that appropriate parameter choices allow for the elimination of redundant multicast transmissions. As a result, the proposed scheme achieves a family of rate memory trade offs with flexible subpacketization. We present numerical comparisons illustrating that the proposed t-scheme outperforms existing hotplug coded caching schemes in certain memory regimes.

Coded Caching for Combinatorial Multi-Access Hotplug Networks from $t$-Designs

TL;DR

This work extends coded caching to a hotplug, combinatorial multi-access setting where each user connects to an r-subset of C caches and only C' caches are online during delivery. It generalizes the HpPDA framework and introduces a t-design–based caching scheme that uses MDS-coded placement and a family of PDAs to manage heterogeneous online cache access, enabling decodability while eliminating redundant multicast transmissions. A key contribution is the characterization of achievable rate–memory trade-offs parameterized by a_{s,j} with decodability guaranteed when Y_j ≤ Y_{j-1}, and the demonstration that setting a_{s,j}=λ^t_s yields uniform access across active users; the framework also specializes to existing CRR schemes for r=1. Numerical results indicate the proposed t-design scheme outperforms certain hotplug benchmarks in specific memory regimes, illustrating practical gains from jointly optimizing hotplug and multi-access structures.

Abstract

We study hotplug coded caching in combinatorial multi-access networks, which generalizes existing hotplug coded caching models by allowing users to access multiple caches, while only a subset of caches is online during the delivery phase. We first generalize the Hotplug Placement Delivery Array (HpPDA) framework to the combinatorial multi-access setting. Based on this generalized framework, we propose a t-design-based coded caching scheme for combinatorial multi-access networks. We characterize a class of design parameters under which every active user has access to a sufficient number of coded subfiles to decode its requested file, and show that appropriate parameter choices allow for the elimination of redundant multicast transmissions. As a result, the proposed scheme achieves a family of rate memory trade offs with flexible subpacketization. We present numerical comparisons illustrating that the proposed t-scheme outperforms existing hotplug coded caching schemes in certain memory regimes.
Paper Structure (14 sections, 8 theorems, 42 equations, 2 figures, 1 algorithm)

This paper contains 14 sections, 8 theorems, 42 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Preliminaries
  3. System Model
  4. Preliminaries
  5. Some Existing Schemes on Hotplug Coded Caching
  6. Main Results
  7. Proposed Hotplug Coded Caching Scheme for Combinatorial Multi-Access Networks
  8. Generalized Multi-Access Hotplug Placement Delivery Arrays
  9. Hotplug Coded Caching Scheme for Combinatorial Multi-Access Networks
  10. Combinatorial Multi-Access Hotplug Coded Caching Using $t$-Designs
  11. Specialization to Existing Schemes
  12. CRR $t$-design scheme CRR
  13. Numerical Comparison
  14. Conclusions

Key Result

Theorem 1

(RR1) Given a $(K, K^{\prime}, F, F^{\prime}, Z, Z^{\prime}, S)$-HpPDA $(P, B)$, there exists a $(K, K^{\prime}, N)$ hotplug coded caching scheme obtaining the following memory-rate pair, where $M\leq N$ denotes the number of files each user can store in it’s cache.

Figures (2)

  • Figure 1: $B_{1,1}$ and $B_{1,2}$
  • Figure 2: Rate per user vs. Caching fraction $\frac{M}{N}$.

Theorems & Definitions (23)

  • Definition 1
  • Definition 2
  • Theorem 1
  • Definition 3
  • Definition 4
  • Theorem 2
  • Theorem 3
  • Corollary 1
  • Theorem 4: $t$-scheme
  • proof
  • ...and 13 more