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Cyclic Wrap-Around Multi-Access Coded Caching with Private Caches

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

TL;DR

For this model, this work proposes a coded caching scheme under uncoded placement, characterize its achievable rate, and derive a cut-set-based lower bound on the optimal worst-case rate.

Abstract

We consider a variant of the coded caching problem where users connect to two types of caches, called private caches and access caches. The problem setting consists of a server having a library of files and a set of access caches. Every user, equipped with a private cache, connects to $L$ neighboring access caches in a cyclic wrap-around fashion. The server populates the private and access caches with file contents in either coded or uncoded format. For this setting, we derive a lower bound on the optimal worst-case transmission rate using cut-set arguments. This lower bound applies to both coded and uncoded placements. We then provide an achievable scheme with uncoded placement and show that our scheme specializes to the well-known Maddah-Ali-Niesen scheme for the dedicated cache network in the absence of access caches. Finally, we show that the proposed scheme achieves optimality in large memory regimes and provide numerical plots comparing the rate of the proposed scheme with the derived lower bound, demonstrating the optimality of our scheme.

Cyclic Wrap-Around Multi-Access Coded Caching with Private Caches

TL;DR

For this model, this work proposes a coded caching scheme under uncoded placement, characterize its achievable rate, and derive a cut-set-based lower bound on the optimal worst-case rate.

Abstract

We consider a variant of the coded caching problem where users connect to two types of caches, called private caches and access caches. The problem setting consists of a server having a library of files and a set of access caches. Every user, equipped with a private cache, connects to neighboring access caches in a cyclic wrap-around fashion. The server populates the private and access caches with file contents in either coded or uncoded format. For this setting, we derive a lower bound on the optimal worst-case transmission rate using cut-set arguments. This lower bound applies to both coded and uncoded placements. We then provide an achievable scheme with uncoded placement and show that our scheme specializes to the well-known Maddah-Ali-Niesen scheme for the dedicated cache network in the absence of access caches. Finally, we show that the proposed scheme achieves optimality in large memory regimes and provide numerical plots comparing the rate of the proposed scheme with the derived lower bound, demonstrating the optimality of our scheme.
Paper Structure (17 sections, 3 theorems, 24 equations, 3 figures, 1 table)

This paper contains 17 sections, 3 theorems, 24 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Our Contributions
  3. System Model and Preliminaries
  4. System Model
  5. MAN Scheme
  6. Main Results
  7. Lower Bound on the Optimal Rate
  8. Achievable Rate
  9. Optimality Result
  10. Achievability Scheme
  11. Motivating Example
  12. Achievability Scheme
  13. Rate-Memory Trade-off Characterization for the Proposed Scheme
  14. Memory Sharing to Achieve Rate for Non-Integral $\gamma_a$ and $\gamma_p$
  15. Optimality in Large Memory Regime
  16. ...and 2 more sections

Key Result

Theorem 1

For the $(K, L, M_a, M_p, N)-$CW-MAP coded caching setting, the following lower bound holds on the optimal worst-case rate: where $p=\min(s+L-1,K).$

Figures (3)

  • Figure 1: System Model
  • Figure 2: Rate vs $M_p$ comparison for the $(K=30,L=3,M_a=6,M_p,N=30)-$CW-MAP coded caching system.
  • Figure 4: Rate vs $M_p$ comparison for the $(K=30,L=3,M_a=8,M_p,N=30)-$CW-MAP coded caching system.

Theorems & Definitions (10)

  • Theorem 1
  • Remark 1
  • Theorem 2
  • Remark 2
  • Lemma 1
  • Example 1
  • Example 2
  • Definition 2
  • Example 3
  • Remark 3