A New Construction Structure on MISO Coded Caching with Linear Subpacketization: Half-Sum Disjoint Packing

2026-01-15

AI Summary

This work addresses the impractical exponential growth of subpacketization in existing coded caching schemes for MISO cache-aided broadcast channels. To overcome this limitation, the authors propose a novel framework based on Latin squares that reformulates the design of multi-antenna placement delivery arrays (MAPDAs) as an L-half-strongly disjoint packing (L-HSDP) combinatorial structure, thereby generalizing the single-antenna NHSDP concept for the first time. The proposed approach achieves linear subpacketization complexity with $F = K$, significantly reducing system overhead while incurring only a minor loss in sum degrees of freedom. Consequently, it outperforms existing linear schemes and strikes an effective balance between low subpacketization and high spatial multiplexing gain.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

In the $(L,K,M,N)$ cache-aided multiple-input single-output (MISO) broadcast channel (BC) system, the server is equipped with $L$ antennas and communicates with $K$ single-antenna users through a wireless broadcast channel where the server has a library containing $N$ files, and each user is equipped with a cache of size $M$ files. Under the constraints of uncoded placement and one-shot linear delivery strategies, many schemes achieve the maximum sum Degree-of-Freedom (sum-DoF). However, for general parameters $L$, $M$, and $N$, their subpacketizations increase exponentially with the number of users. We aim to design a MISO coded caching scheme that achieves a large sum-DoF with low subpacketization $F$. An interesting combinatorial structure, called the multiple-antenna placement delivery array (MAPDA), can be used to generate MISO coded caching schemes under these two strategies; moreover, all existing schemes with these strategies can be represented by the corresponding MAPDAs. In this paper, we study the case with $F=K$ (i.e., $F$ grows linearly with $K$) by investigating MAPDAs. Specifically, based on the framework of Latin squares, we transform the design of MAPDA with $F=K$ into the construction of a combinatorial structure called the $L$-half-sum disjoint packing (HSDP). It is worth noting that a $1$-HSDP is exactly the concept of NHSDP, which is used to generate the shared-link coded caching scheme with $F=K$. By constructing $L$-HSDPs, we obtain a class of new schemes with $F=K$. Finally, theoretical and numerical analyses show that our $L$-HSDP schemes significantly reduce subpacketization compared to existing schemes with exponential subpacketization, while only slightly sacrificing sum-DoF, and achieve both a higher sum-DoF and lower subpacketization than the existing schemes with linear subpacketization.

Problem

• MISO coded caching
• subpacketization
• sum-DoF
• cache-aided broadcast channel
• combinatorial design

Innovation

• MISO coded caching
• linear subpacketization
• half-sum disjoint packing
• placement delivery array
• sum-DoF