发表机构
Southeast University（东南大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种提升方法，通过重新编码安全单接入方案的缓存并复用其多播消息，构造安全多接入编码缓存方案，达到最小存储并证明近似最优性。
AI 中文摘要
我们通过重新编码安全单接入方案的缓存并原样复用其多播消息，构造了安全循环多接入编码缓存方案。对于一个包含 $N$ 个文件的库，$K$ 个用户中的每个用户读取 $L<K$ 个连续的共享缓存，并且必须在恢复其请求文件的同时不学习关于其他文件的任何信息。从一个具有其缓存符号循环表示的父方案出发，该变换使得每个访问窗口能够恢复对应的父缓存符号，并且在这些符号条件下，不学习关于剩余符号的任何信息。一个确定性的帕斯卡窗口编码器处理连续出现跨越至少 $L$ 个用户的符号。一个随机化的互补对偶编码器处理较短的跨度。在适当的有限域上，这些编码器在块可分离、父保持类中，对于每个输入长度达到精确的最小每块存储。将该变换应用于两个安全单接入方案，为 $N,K\ge2$ 和 $1\le L<K$ 给出一个可达到的记忆率族，包括精确的速率一缓存大小 $(N-1)(K-1)/L$。使用任意安全多接入方案的逆界，我们证明了可达到族的近似保证，并给出了精确的 $L=K-1$ 权衡的证明。
英文摘要
We construct secure cyclic multi-access coded caching schemes by re-encoding the caches of a secure single-access scheme and reusing its multicast message unchanged. For a library of $N$ files, each of $K$ users reads $L<K$ consecutive shared caches and must recover its requested file while learning no information about the other files. Starting from a parent scheme with a cyclic representation of its cached symbols, the transformation lets each access window recover the corresponding parent-cache symbols and, conditioned on them, learn nothing about the remaining symbols. A deterministic Pascal-window encoder handles symbols whose consecutive appearances span at least $L$ users. A randomized complement-dual encoder handles shorter spans. Over a suitable finite field, these encoders attain the exact minimum per-block storage for every input length in the block-separable, parent-preserving class. Applying the transformation to two secure single-access schemes gives an achievable memory-rate family for $N,K\ge2$ and $1\le L<K$, including the exact rate-one cache size $(N-1)(K-1)/L$. Using converse bounds for arbitrary secure multi-access schemes, we prove approximation guarantees for the achievable family and give a proof of the exact $L=K-1$ tradeoff.
Comments48 pages, 2 figures. This paper was presented in part at the 2024 IEEE Information Theory Workshop(ITW)
