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Multi-Antenna Coded Caching for Multi-Access Networks with Cyclic Wrap-Around

Elizabath Peter, K. K. Krishnan Namboodiri, B. Sundar Rajan

TL;DR

This work extends multi-access coded caching to a multi-antenna server in a cyclic wrap-around topology by introducing caching and delivery arrays and four systematic constructions. It shows that, under uncoded placement and one-shot delivery, the normalized delivery time can achieve $T_n = \frac{K-rt}{rt+L}$ in many regimes, with substantial subpacketization reductions when $\gcd(K,t,L) \neq 1$ via gcd-based reductions and EPDA-based methods. The optimality of several schemes is established by comparison to the corresponding multi-antenna dedicated cache network, and a special case subsumes single-antenna MACC; Construction IV further generalizes to obtain MACC schemes from any EPDA. The results unify array-based design for MACC with multi-antenna capabilities and illuminate tradeoffs between delivery time, memory, and subpacketization, while pointing to future work on finite-SNR performance and broader network models.

Abstract

This work explores a multiple transmit antenna setting in a multi-access coded caching (MACC) network where each user accesses more than one cache. A MACC network has $K$ users and $K$ caches, and each user has access to $r < K$ consecutive caches in a cyclic wrap-around manner. There are $L$ antennas at the server, and each cache has a normalized size of $M/N \leq 1$. The cyclic wrap-around MACC network with a single antenna at the server has been a well-investigated topic, and several coded caching schemes and improved lower bounds on the performance are known for the same. However, this MACC network has not yet been studied under multi-antenna settings in the coded caching literature. We study the multi-antenna MACC problem and propose a solution for the same by constructing a pair of arrays called caching and delivery arrays. We present three constructions of caching and delivery arrays for different scenarios and obtain corresponding multi-antenna MACC schemes for the same. Two schemes resulting from the above constructions achieve optimal performance under uncoded placement and one-shot delivery. The optimality is shown by matching the performance of the multi-antenna MACC scheme to that of an optimal multi-antenna scheme for a dedicated cache network having an identical number of users, and each user has a normalized cache size of $rM/N$. Further, as a special case, one of the proposed schemes subsumes an existing optimal MACC scheme for the single-antenna setting.

Multi-Antenna Coded Caching for Multi-Access Networks with Cyclic Wrap-Around

TL;DR

This work extends multi-access coded caching to a multi-antenna server in a cyclic wrap-around topology by introducing caching and delivery arrays and four systematic constructions. It shows that, under uncoded placement and one-shot delivery, the normalized delivery time can achieve in many regimes, with substantial subpacketization reductions when via gcd-based reductions and EPDA-based methods. The optimality of several schemes is established by comparison to the corresponding multi-antenna dedicated cache network, and a special case subsumes single-antenna MACC; Construction IV further generalizes to obtain MACC schemes from any EPDA. The results unify array-based design for MACC with multi-antenna capabilities and illuminate tradeoffs between delivery time, memory, and subpacketization, while pointing to future work on finite-SNR performance and broader network models.

Abstract

This work explores a multiple transmit antenna setting in a multi-access coded caching (MACC) network where each user accesses more than one cache. A MACC network has users and caches, and each user has access to consecutive caches in a cyclic wrap-around manner. There are antennas at the server, and each cache has a normalized size of . The cyclic wrap-around MACC network with a single antenna at the server has been a well-investigated topic, and several coded caching schemes and improved lower bounds on the performance are known for the same. However, this MACC network has not yet been studied under multi-antenna settings in the coded caching literature. We study the multi-antenna MACC problem and propose a solution for the same by constructing a pair of arrays called caching and delivery arrays. We present three constructions of caching and delivery arrays for different scenarios and obtain corresponding multi-antenna MACC schemes for the same. Two schemes resulting from the above constructions achieve optimal performance under uncoded placement and one-shot delivery. The optimality is shown by matching the performance of the multi-antenna MACC scheme to that of an optimal multi-antenna scheme for a dedicated cache network having an identical number of users, and each user has a normalized cache size of . Further, as a special case, one of the proposed schemes subsumes an existing optimal MACC scheme for the single-antenna setting.
Paper Structure (16 sections, 6 theorems, 40 equations, 6 figures, 1 table, 1 algorithm)

This paper contains 16 sections, 6 theorems, 40 equations, 6 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System and Channel Model
  3. Preliminaries
  4. Main Results
  5. Caching and Delivery Arrays
  6. Construction I
  7. An approach to reduce subpacketization level when $\gcd(K,t,L)\neq 1$
  8. Constructions II and III
  9. When $\gcd(K,t)\neq 1$ in Theorem \ref{['thm1']}
  10. A further generalization of Theorem \ref{['thm1']}
  11. Construction IV
  12. Performance Comparison and Analyses
  13. Comparison with the scheme in CWLZC when $L=1$
  14. Comparison with the scheme in CBWC
  15. Normalized delivery time versus memory tradeoff of the scheme in Theorem \ref{['thm_general']}
  16. ...and 1 more sections

Key Result

Theorem 1

Corresponding to any $(K,L,F,Z,S)$ EPDA, there exists a multi-antenna coded caching scheme for the dedicated cache network with $K$ users, $L$ transmit antennas, and ${M}/{N}={Z}/{F}$. Furthermore, the server can meet any user demand $\mathbf{d}$ with an NDT $T_n = {S}/{F}$.

Figures (6)

  • Figure 1: Cyclic wrap-around MACC network with multiple transmit antennas.
  • Figure 2: Caching and delivery arrays for $K=7$, $N=7$, $r=2$, $L=3$, $t=2$.
  • Figure 3: Caching and delivery arrays for $K=7$, $N=7$, $r=2$, $L=3$, $t=1$.
  • Figure 4: Caching and delivery arrays for $K=10$, $r=2$, $L=4$, $t=2$.
  • Figure 5: Cyclic wrap-around MACC schemes: $K=25$, $N=25$, $r=3$, $L=1$
  • ...and 1 more figures

Theorems & Definitions (17)

  • Definition 1: Extended Placement Delivery Array NPRYWCQC
  • Theorem 1: NPR
  • Definition 2: Caching array
  • Definition 3: Delivery array
  • Lemma 1
  • Theorem 2
  • Remark 1
  • Example 1
  • Theorem 3
  • Remark 2
  • ...and 7 more