Symmetric multilevel diversity coding (SMDC) is a source coding problem where the independent sources are ordered according to their importance. It was shown that separately encoding independent sources (referred to as ``\textit{superposition coding}") is optimal. In this paper, we consider an $(L,s)$ \textit{sliding secure} SMDC problem with security priority, where each source $X_{\alpha}~(s\leq \alpha\leq L)$ is kept perfectly secure if no more than $\alpha-s$ encoders are accessible. The reconstruction requirements of the $L$ sources are the same as classical SMDC. A special case of an $(L,s)$ sliding secure SMDC problem that the first $s-1$ sources are constants is called the $(L,s)$ \textit{multilevel secret sharing} problem. For $s=1$, the two problems coincide, and we show that superposition coding is optimal. The rate regions for the $(3,2)$ problems are characterized. It is shown that superposition coding is suboptimal for both problems. The main idea that joint encoding can reduce coding rates is that we can use the previous source $X_{\alpha-1}$ as the secret key of $X_{\alpha}$. Based on this idea, we propose a coding scheme that achieves the minimum sum rate of the general $(L,s)$ multilevel secret sharing problem. Moreover, superposition coding of the $s$ sets of sources $X_1$, $X_2$, $\cdots$, $X_{s-1}$, $(X_s, X_{s+1}, \cdots, X_L)$ achieves the minimum sum rate of the general sliding secure SMDC problem.

翻译：对称多级多样性编码（SMDC）是一类源编码问题，其中独立信源根据其重要程度排序。已有研究表明，对独立信源进行独立编码（称为“叠加编码”）具有最优性。本文考虑具有安全优先级约束的$(L,s)$滑动安全SMDC问题：当可访问的编码器数量不超过$\alpha-s$时，每个信源$X_{\alpha}~(s\leq \alpha\leq L$均需保持完美安全性，同时$L$个信源的重构需求与经典SMDC相同。当$(L,s)$滑动安全SMDC问题中前$s-1$个信源为常数时，该特例被称为$(L,s)$多级秘密共享问题。对于$s=1$的情形，两类问题等价，我们证明此时叠加编码仍具有最优性。文章完整刻画了$(3,2)$场景的码率区域，并证明叠加编码在该场景中两类问题均非最优。联合编码可降低码率的核心思想在于：可利用前一信源$X_{\alpha-1}$作为$X_{\alpha}$的秘密密钥。基于此思想，我们提出一种能实现通用$(L,s)$多级秘密共享问题最小和码率的编码方案。此外，对$s$组信源$X_1$、$X_2$、$\cdots$、$X_{s-1}$、$(X_s, X_{s+1}, \cdots, X_L)$采用叠加编码即可实现通用滑动安全SMDC问题的最小和码率。