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Asymmetric Stream Allocation and Linear Decodability in MIMO Coded Caching

Mohammad NaseriTehrani, MohammadJavad Salehi, Antti Tölli

TL;DR

A heuristic MIMO-CC delivery and scheduling framework that enables asymmetric stream allocation while adhering to linear decodability, thereby expanding the feasibility region of achievable DoF compared to symmetric-constrained designs is proposed.

Abstract

Coded caching (CC) can transform cache memory at network devices into an active communication resource. Prior studies have shown that CC can significantly enhance the achievable Degrees of Freedom (DoF) in multi-input multi-output (MIMO) systems. To fully exploit MIMO-CC gains across all SNR regimes and enable practical linear receivers, flexible scheduling is required. Existing DoF analysis, scheduling, and linear receiver design, however, largely assume symmetric stream allocations across users. This paper extends the authors' recent work on DoF and linear decodability analysis for MIMO-CC systems by deriving a simple criterion, based on per-user stream allocation, that guarantees linear decodability for both symmetric and non-symmetric bit-level CC schemes. Building on this, we propose a heuristic MIMO-CC delivery and scheduling framework that enables asymmetric stream allocation while adhering to linear decodability, thereby expanding the feasibility region of achievable DoF compared to symmetric-constrained designs.

Asymmetric Stream Allocation and Linear Decodability in MIMO Coded Caching

TL;DR

A heuristic MIMO-CC delivery and scheduling framework that enables asymmetric stream allocation while adhering to linear decodability, thereby expanding the feasibility region of achievable DoF compared to symmetric-constrained designs is proposed.

Abstract

Coded caching (CC) can transform cache memory at network devices into an active communication resource. Prior studies have shown that CC can significantly enhance the achievable Degrees of Freedom (DoF) in multi-input multi-output (MIMO) systems. To fully exploit MIMO-CC gains across all SNR regimes and enable practical linear receivers, flexible scheduling is required. Existing DoF analysis, scheduling, and linear receiver design, however, largely assume symmetric stream allocations across users. This paper extends the authors' recent work on DoF and linear decodability analysis for MIMO-CC systems by deriving a simple criterion, based on per-user stream allocation, that guarantees linear decodability for both symmetric and non-symmetric bit-level CC schemes. Building on this, we propose a heuristic MIMO-CC delivery and scheduling framework that enables asymmetric stream allocation while adhering to linear decodability, thereby expanding the feasibility region of achievable DoF compared to symmetric-constrained designs.
Paper Structure (6 sections, 2 theorems, 13 equations, 6 figures, 2 algorithms)

This paper contains 6 sections, 2 theorems, 13 equations, 6 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Linear Decodability for MIMO-CC
  4. Asymmetric Multicast MIMO-CC Scheduling
  5. Simulation Results
  6. Conclusion

Key Result

Theorem 1

With the transmission model in eq:general_trans_vector, linear decoding of $\beta_k(i)$ streams is possible at each user $k \in {\mathcal{K}}(i)$ in interval $i$ if the parameters $\theta_{\mathcal{T}}(i)$ and $\beta_k(i)$ satisfy

Figures (6)

  • Figure 1: MIMO-CC scheduling: serving arbitrary $\Omega$ users per interval, each receiving asymmetric streams $\beta_k(s)\leq G$ per sub-interval.
  • Figure 2: Example 1: $\Omega$=5, $t$=1, $L$=10, $G$=3; a) symmetric scheduling, b) replicated symmetric table with $\tilde{\delta}$, c) asymmetric scheduling table.
  • Figure 3: Achievable DoF enhancement, $L=11$, $G=8$, $t\in\{1,2,3\}$, $\Omega\in\{4,6,8\}$.
  • Figure 4: The effect of the proposed asymmetric scheduling, $t=1$, $L=10$, $G=3$.
  • Figure 5: The effect of the proposed asymmetric scheduling, $t=2, L=11, G=8$.
  • ...and 1 more figures

Theorems & Definitions (6)

  • Theorem 1
  • proof
  • Example 1
  • Lemma 1
  • proof
  • Example 2