A New Construction Structure on MISO Coded Caching with Linear Subpacketization: Half-Sum Disjoint Packing
Bowen Zheng, Minquan Cheng, Kai Wan, Giuseppe Caire
TL;DR
This work advances MISO coded caching by introducing L-HSDP, a generalization of NHSDP, to construct MAPDAs with linear subpacketization F=K. By leveraging Latin squares and a high-dimensional embedding framework, the authors build L-$(v,g,b)$ HSDPs that yield MAPDAs with memory ratio M/N=1-bg/v and sum-DoF g, while keeping subpacketization minimal. Theoretical and numerical analyses show that L-HSDP-based schemes achieve substantial reductions in subpacketization with only modest DoF loss compared to exponential schemes, and can outperform existing linear-subpacketization schemes in several regimes. This framework thus offers a practical, scalable path to high-throughput, low-complexity cache-aided MISO communications.
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.