论文标题
组合多访问编码的缓存：通过编码放置的提高速率记忆折衷
Combinatorial Multi-Access Coded Caching: Improved Rate-Memory Trade-off with Coded Placement
论文作者
论文摘要
这项工作考虑了Muralidhar \ textit {et al。}的最新作品中引入的组合多访问编码的缓存问题[P. N. Muralidhar，D。Katyal和B. S. Rajan，``Maddah-Ali-niesen用于多访问编码的缓存计划，''理论研讨会（ITW）}，2021]问题设置由一个中央服务器组成，其中一个库$ n $文件和$ c $ caches每个带有$ m $的库。系统中的每个用户都可以访问$ r <c $ caches的唯一集，并且存在与每一个不同集合$ r $ caches相对应的用户。因此，系统中的用户数为$ \ binom {c} {r} $。对于上述组合多访问设置，我们建议使用基于MDS代码的编码放置的编码缓存方案。与在$ m> n/c $时，这种新颖的放置技术有助于在未编码放置下的最佳方案中获得更高的速率。对于较低的内存制度，我们提出了另一种带有编码位置的方案，如果文件数量不超过用户数量，则在未编码的位置下优于最佳方案。此外，我们在组合多访问编码的缓存方案的最佳速率内存权衡方面得出了信息理论下限。此外，使用派生的下限，我们证明了第一个方案在较高的内存制度中是最佳的，如果$ n \ leq \ binom {c} {r} $，则第二个方案是最佳的。最后，我们表明，当$ r = 2 $时，第一个方案的性能在最佳性能的恒定因素之内。
This work considers the combinatorial multi-access coded caching problem introduced in the recent work by Muralidhar \textit{et al.} [P. N. Muralidhar, D. Katyal, and B. S. Rajan, ``Maddah-Ali-Niesen scheme for multi-access coded caching,'' in \textit{IEEE Inf. Theory Workshop (ITW)}, 2021] The problem setting consists of a central server having a library of $N$ files and $C$ caches each with capacity $M$. Each user in the system can access a unique set of $r<C$ caches, and there exist users corresponding to every distinct set of $r$ caches. Therefore, the number of users in the system is $\binom{C}{r}$. For the aforementioned combinatorial multi-access setting, we propose a coded caching scheme with an MDS code-based coded placement. This novel placement technique helps to achieve a better rate in the delivery phase compared to the optimal scheme under uncoded placement when $M> N/C$. For a lower memory regime, we present another scheme with coded placement, which outperforms the optimal scheme under uncoded placement if the number of files is no more than the number of users. Further, we derive an information-theoretic lower bound on the optimal rate-memory trade-off of the combinatorial multi-access coded caching scheme. In addition, using the derived lower bound, we show that the first scheme is optimal in the higher memory regime, and the second scheme is optimal if $N\leq \binom{C}{r}$. Finally, we show that the performance of the first scheme is within a constant factor of the optimal performance, when $r=2$.
