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D2D Coded Caching from Two Classes of Optimal DPDAs using Cross Resolvable Designs

Rashid Ummer N. T., B. Sundar Rajan

TL;DR

This paper first constructed three classes of DPDAs using a cross resolvable design, a group divisible design, and a newly developed block design that achieve low subpacketization levels while meeting the known lower bound on the transmission load of a DPDA.

Abstract

Device to device (D2D) communication is one of the most promising techniques for fifth-generation and beyond wireless communication systems. This paper considers coded caching in a wireless D2D network, in which a central server initially places the data in the user cache memories, and all user demands are served through inter-user coded multicast transmissions. D2D placement delivery array (DPDA) was proposed as a tool for designing coded caching schemes with reduced subpacketization levels in a D2D network. In this paper, we first constructed three classes of DPDAs using a cross resolvable design, a group divisible design, and a newly developed block design. The resulting D2D schemes achieve low subpacketization levels while meeting the known lower bound on the transmission load of a DPDA. These classes of constructed DPDAs either simplify or generalize all existing DPDA constructions that achieve the known lower bound and have low subpacketization levels. Furthermore, a new lower bound on the transmission load of a DPDA is proposed. Two new classes of DPDAs are then constructed using a cross resolvable design and a newly developed block design, respectively. These constructions yield low-subpacketization D2D schemes and achieve the proposed lower bound on the transmission load. Compared to existing schemes with the same system parameters as those obtained from the proposed DPDAs, the proposed schemes have an advantage in either transmission load or subpacketization level or both.

D2D Coded Caching from Two Classes of Optimal DPDAs using Cross Resolvable Designs

TL;DR

This paper first constructed three classes of DPDAs using a cross resolvable design, a group divisible design, and a newly developed block design that achieve low subpacketization levels while meeting the known lower bound on the transmission load of a DPDA.

Abstract

Device to device (D2D) communication is one of the most promising techniques for fifth-generation and beyond wireless communication systems. This paper considers coded caching in a wireless D2D network, in which a central server initially places the data in the user cache memories, and all user demands are served through inter-user coded multicast transmissions. D2D placement delivery array (DPDA) was proposed as a tool for designing coded caching schemes with reduced subpacketization levels in a D2D network. In this paper, we first constructed three classes of DPDAs using a cross resolvable design, a group divisible design, and a newly developed block design. The resulting D2D schemes achieve low subpacketization levels while meeting the known lower bound on the transmission load of a DPDA. These classes of constructed DPDAs either simplify or generalize all existing DPDA constructions that achieve the known lower bound and have low subpacketization levels. Furthermore, a new lower bound on the transmission load of a DPDA is proposed. Two new classes of DPDAs are then constructed using a cross resolvable design and a newly developed block design, respectively. These constructions yield low-subpacketization D2D schemes and achieve the proposed lower bound on the transmission load. Compared to existing schemes with the same system parameters as those obtained from the proposed DPDAs, the proposed schemes have an advantage in either transmission load or subpacketization level or both.
Paper Structure (21 sections, 17 theorems, 20 equations, 8 figures, 4 tables, 2 algorithms)

This paper contains 21 sections, 17 theorems, 20 equations, 8 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. D2D Coded caching network model
  4. PDA and DPDA
  5. Known D2D coded caching schemes
  6. Preliminaries of Combinatorial Design
  7. Lower bound on the transmission load of a DPDA
  8. Proposed DPDA Constructions and Performance Analysis
  9. Construction I
  10. Construction II
  11. Construction III
  12. Construction IV
  13. Construction V
  14. Conclusion
  15. Proof of Corollary \ref{['cor:CRD']}
  16. ...and 6 more sections

Key Result

Theorem 1

( JMQX) For a given $(K, F, Z, S)$ DPDA $\mathbf{P}=(p_{j,k})_{F \times K}$, a $(K,M,N)$ D2D coded caching scheme can be obtained with subpacketization $F$ and $\frac{M}{N}=\frac{Z}{F}$ using Algorithm d2d_alg. For any demand $\vec{d}$, the demands of all users are satisfied with a transmission load

Figures (8)

  • Figure 1: D2D coded caching network model.
  • Figure 2: $(6,9,3,18)$ DPDA in Example \ref{['ex:dpda_eg1']}
  • Figure 3: $(12,9,3,36)$ DPDA in Example \ref{['eg:conc1_gen']}
  • Figure 4: $(8,24,18,8)$ DPDA in Example \ref{['ex:dpda4']}
  • Figure 5: $(5,15,9,10)$ DPDA in Example \ref{['ex:dpda5']}
  • ...and 3 more figures

Theorems & Definitions (46)

  • Definition 1
  • Definition 2
  • Theorem 1
  • Example 1
  • Definition 3: Design $(\mathcal{X}, \mathcal{A})$
  • Definition 4: Resolvable design
  • Definition 5: Cross Resolvable Design
  • Example 2
  • Corollary 1
  • Example 3
  • ...and 36 more