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Coded Caching for Hierarchical Two-Layer Networks with Coded Placement

Rajlaxmi Pandey, Charul Rajput, B. Sundar Rajan

TL;DR

This work tackles hierarchical coded caching in a two-layer network (server–mirrors–users) by introducing a coded-placement scheme that splits each file into a CFL-based first subfile and an MN-based second subfile. By combining these two placement-delivery paradigms and enabling memory sharing, it derives explicit rate expressions for R_1 and R_2 and a composite rate overline{R} = R_1 + K_1 R_2, alongside a global memory metric overline{M} = K_1 M_1 + K_1 K_2 M_2; it also considers a concurrent-transmission setting with a coding delay T. The paper demonstrates, through theoretical analyses and comparisons with KNMD, ZWXWLL, ZWXWL, WWCY, and KWC schemes, that the proposed CFL-MN hybrid achieves lower composite rates across many memory configurations and provides a memory-sharing framework to interpolate between schemes. A specialized single-mirror variant further improves performance in that case. Overall, the work advances practical coded caching for hierarchical networks by optimizing cross-layer caching and offering richer performance diagnostics via composite metrics.

Abstract

We examine a two-layered hierarchical coded caching problem, a configuration addressed in existing research. This involves a server connected to $K_1$ mirrors, each of which serves $K_2$ users. The mirrors and the users are equipped with caches of size $M_1$ and $M_2$, respectively. We propose a hierarchical coded caching scheme with coded placements that outperforms existing schemes. To ensure a fair comparison, we introduce the notion of composite rate, defined as $\overline{R} = R_1 + K_1 R_2$, where $R_1$ is the rate from the server to mirrors and $R_2$ is the rate from mirrors to users. The composite rate has not been discussed before in the literature and is pertinent when mirrors transmit with different carrier frequencies. For the proposed scheme, we show a trade-off between the global memory $\overline{M}=K_1M_1+K_1K_2M_2$ of the system and the composite rate and compare with the existing schemes. Additionally, we conduct this comparative analysis by plotting $R_1$ + $R_2$ against global memory, which is particularly beneficial for systems wherein each mirror can utilize the same carrier frequency, given their significant spatial separation. Additionally, we propose an optimized scheme for the specific case of a single mirror, showing improved performance in this scenario.

Coded Caching for Hierarchical Two-Layer Networks with Coded Placement

TL;DR

This work tackles hierarchical coded caching in a two-layer network (server–mirrors–users) by introducing a coded-placement scheme that splits each file into a CFL-based first subfile and an MN-based second subfile. By combining these two placement-delivery paradigms and enabling memory sharing, it derives explicit rate expressions for R_1 and R_2 and a composite rate overline{R} = R_1 + K_1 R_2, alongside a global memory metric overline{M} = K_1 M_1 + K_1 K_2 M_2; it also considers a concurrent-transmission setting with a coding delay T. The paper demonstrates, through theoretical analyses and comparisons with KNMD, ZWXWLL, ZWXWL, WWCY, and KWC schemes, that the proposed CFL-MN hybrid achieves lower composite rates across many memory configurations and provides a memory-sharing framework to interpolate between schemes. A specialized single-mirror variant further improves performance in that case. Overall, the work advances practical coded caching for hierarchical networks by optimizing cross-layer caching and offering richer performance diagnostics via composite metrics.

Abstract

We examine a two-layered hierarchical coded caching problem, a configuration addressed in existing research. This involves a server connected to mirrors, each of which serves users. The mirrors and the users are equipped with caches of size and , respectively. We propose a hierarchical coded caching scheme with coded placements that outperforms existing schemes. To ensure a fair comparison, we introduce the notion of composite rate, defined as , where is the rate from the server to mirrors and is the rate from mirrors to users. The composite rate has not been discussed before in the literature and is pertinent when mirrors transmit with different carrier frequencies. For the proposed scheme, we show a trade-off between the global memory of the system and the composite rate and compare with the existing schemes. Additionally, we conduct this comparative analysis by plotting + against global memory, which is particularly beneficial for systems wherein each mirror can utilize the same carrier frequency, given their significant spatial separation. Additionally, we propose an optimized scheme for the specific case of a single mirror, showing improved performance in this scenario.
Paper Structure (34 sections, 8 theorems, 99 equations, 12 figures, 2 tables)

This paper contains 34 sections, 8 theorems, 99 equations, 12 figures, 2 tables.

Table of Contents

  1. Introduction and Background
  2. System model
  3. Prior Work
  4. Our Contributions
  5. Organization
  6. Notations
  7. Proposed Coded Caching Scheme for Hierarchical Network
  8. Placement phase
  9. Delivery phase
  10. Proof of correctness
  11. Mirror gets from the server what it transmits to users:
  12. All users get their desired files:
  13. Rate
  14. Memory Sharing
  15. Coding Delay
  16. ...and 19 more sections

Key Result

Theorem 1

If three memory rate points $\mathbf{A}(M_{1}^{A}, M_{2}^{A}, R_{1}^{A}), \mathbf{B}(M_{1}^{B}, M_{2}^{B}, R_{1}^{B}),$ and $\mathbf{C}(M_{1}^{C}, M_{2}^{C}, R_{1}^{C})$ are achievable by a scheme, then any point $\mathbf{P}(M_{1}, M_{2}, R_{1})$ in the convex hull of $\mathbf{A}, \mathbf{B},$ and $

Figures (12)

  • Figure 1: Hierarchical two-layer network.
  • Figure 2: Convex hull for memory sharing.
  • Figure 3: Global memory and composite rate for $N \leq K$
  • Figure 4: Global memory and composite rate for $N > K$
  • Figure 5: Performance comparison for a ($3,2$;$M_{1}$,$M_{2}$;6) hierarchical caching system in Example \ref{['ex1']}
  • ...and 7 more figures

Theorems & Definitions (17)

  • Theorem 1
  • Example 1
  • Example 2
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Corollary 1
  • Example 3
  • Example 4
  • Example 5
  • ...and 7 more