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 $r=2$.

翻译：本文研究了Muralidhar等人近期工作中提出的组合多接入编码缓存问题[P. N. Muralidhar, D. Katyal, and B. S. Rajan, “Maddah-Ali-Niesen scheme for multi-access coded caching,” in 《IEEE信息理论研讨会(ITW)》, 2021]。该问题设置包括一个拥有$N$个文件库的中心服务器和$C$个缓存器，每个缓存器容量为$M$。系统中的每个用户可以访问一组唯一的$r<C$个缓存器，并且存在与每个不同的$r$个缓存器集合相对应的用户。因此，系统中的用户数量为$\binom{C}{r}$。针对上述组合多接入设置，我们提出了一种基于MDS码的编码放置的编码缓存方案。这种新颖的放置技术有助于在交付阶段实现比$M> N/C$时未编码放置下的最优方案更好的速率。对于较低内存范围，我们提出了另一种编码放置方案，当文件数量不超过用户数量时，该方案优于未编码放置下的最优方案。此外，我们推导了组合多接入编码缓存方案的最优速率-内存权衡的信息论下界。利用推导的下界，我们证明了第一个方案在较高内存范围内是最优的，而第二个方案在$N\leq \binom{C}{r}$条件下是最优的。最后，我们证明当$r=2$时，第一个方案的性能在最优性能的常数因子范围内。