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Multiaccess Coded Caching with Heterogeneous Retrieval Costs

Wenbo Huang, Minquan Cheng, Kai Wan, Xiaojun Li, Robert Caiming Qiu, Giuseppe Caire

TL;DR

This work addresses the problem of minimizing total communication cost in a multiaccess coded caching (MACC) system under heterogeneous retrieval costs for accessing cache nodes and a per-broadcast cost. It introduces a cost-aware MACC framework based on superposition coding that layers MACC schemes across access levels, and derives an optimization problem over weights and cache-division parameters to minimize the total cost. A key theoretical finding is a sparsity property: the optimal solution has at most two nonzero weight components, which enables a structure-aware algorithm using a two-variable SQP subproblem and a greedy index search with warm-starts. Empirical results show the proposed scheme outperforms prior MACC schemes in heterogeneous-cost settings, offering more stable performance across varying retrieval costs and levels of access, with practical implications for edge/fog networks where cache-access costs are non-negligible.

Abstract

The multiaccess coded caching (MACC) system, as formulated by Hachem {\it et al.}, consists of a central server with a library of $N$ files, connected to $K$ cache-less users via an error-free shared link, and $K$ cache nodes, each equipped with cache memory of size $M$ files. Each user can access $L$ neighboring cache nodes under a cyclic wrap-around topology. Most existing studies operate under the strong assumption that users can retrieve content from their connected cache nodes at no communication cost. In practice, each user retrieves content from its $L$ different connected cache nodes at varying costs. Additionally, the server also incurs certain costs to transmit the content to the users. In this paper, we focus on a cost-aware MACC system and aim to minimize the total system cost, which includes cache-access costs and broadcast costs. Firstly, we propose a novel coded caching framework based on superposition coding, where the MACC schemes of Cheng \textit{et al.} are layered. Then, a cost-aware optimization problem is derived that optimizes cache placement and minimizes system cost. By identifying a sparsity property of the optimal solution, we propose a structure-aware algorithm with reduced complexity. Simulation results demonstrate that our proposed scheme consistently outperforms the scheme of Cheng {\it et al.} in scenarios with heterogeneous retrieval costs.

Multiaccess Coded Caching with Heterogeneous Retrieval Costs

TL;DR

This work addresses the problem of minimizing total communication cost in a multiaccess coded caching (MACC) system under heterogeneous retrieval costs for accessing cache nodes and a per-broadcast cost. It introduces a cost-aware MACC framework based on superposition coding that layers MACC schemes across access levels, and derives an optimization problem over weights and cache-division parameters to minimize the total cost. A key theoretical finding is a sparsity property: the optimal solution has at most two nonzero weight components, which enables a structure-aware algorithm using a two-variable SQP subproblem and a greedy index search with warm-starts. Empirical results show the proposed scheme outperforms prior MACC schemes in heterogeneous-cost settings, offering more stable performance across varying retrieval costs and levels of access, with practical implications for edge/fog networks where cache-access costs are non-negligible.

Abstract

The multiaccess coded caching (MACC) system, as formulated by Hachem {\it et al.}, consists of a central server with a library of files, connected to cache-less users via an error-free shared link, and cache nodes, each equipped with cache memory of size files. Each user can access neighboring cache nodes under a cyclic wrap-around topology. Most existing studies operate under the strong assumption that users can retrieve content from their connected cache nodes at no communication cost. In practice, each user retrieves content from its different connected cache nodes at varying costs. Additionally, the server also incurs certain costs to transmit the content to the users. In this paper, we focus on a cost-aware MACC system and aim to minimize the total system cost, which includes cache-access costs and broadcast costs. Firstly, we propose a novel coded caching framework based on superposition coding, where the MACC schemes of Cheng \textit{et al.} are layered. Then, a cost-aware optimization problem is derived that optimizes cache placement and minimizes system cost. By identifying a sparsity property of the optimal solution, we propose a structure-aware algorithm with reduced complexity. Simulation results demonstrate that our proposed scheme consistently outperforms the scheme of Cheng {\it et al.} in scenarios with heterogeneous retrieval costs.
Paper Structure (14 sections, 4 theorems, 31 equations, 3 figures, 1 algorithm)

This paper contains 14 sections, 4 theorems, 31 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Multiaccess Caching Model with Heterogeneous Retrieval Costs
  4. MACC Scheme
  5. Main Results
  6. Superposition MACC scheme
  7. Structure-aware Algorithm
  8. Property of the Optimal Solution
  9. Optimization Algorithm
  10. Performance Analysis
  11. Conclusion
  12. Example for Construction \ref{['constr-3-arrays']}
  13. MACC Scheme with Costs
  14. Communication Cost Formulation

Key Result

Lemma 1

The transmission generated by eq-delivery-strategy is of the one-shot type if, for every two different entries $\mathbf{Q}(j_1,k_1)$ and $\mathbf{Q}(j_2,k_2)$ in $\mathbf{Q}$, when $\mathbf{Q}(j_1,k_1) = \mathbf{Q}(j_2,k_2) = s$ is an integer, the following conditions hold. $\square$

Figures (3)

  • Figure 1: The $(K,L,M,N,\rho,v)$ multiaccess coded caching system.
  • Figure 2: Performance comparison between the baseline Scheme and the proposed superposition scheme.
  • Figure 3: An example of $\mathbf{C}^{(1)}, \mathbf{U}^{(1)}, \mathbf{Q}^{(1)}$ under system parameters $(8,3,2,8)$.

Theorems & Definitions (6)

  • Lemma 1: yan2017placement
  • Lemma 2: MAC
  • Theorem 1
  • Proposition 1: Two-Point Structure of the Optimal Solution
  • proof
  • Example 1