Weakly Secure Symmetric Multilevel Diversity Coding
Weakly Secure Symmetric Multilevel Diversity Coding
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DOI：
10.1109/tit.2020.3004482
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发表时间：
2020-06
影响因子：
2.5
通讯作者：
Tao Guo;C. Tian;Tie Liu;R. Yeung
中科院分区：
文献类型：
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作者：
Tao Guo;C. Tian;Tie Liu;R. Yeung
多级分集编码是一种经典的编码模型，其中对多个相互独立的信息消息进行编码，从而可以对不同的消息提供不同的可靠性要求。众所周知，叠加编码，即对独立消息进行单独编码，对于对称多级分集编码（SMDC）来说是最佳的（Yeung-Zhang 1999）。在本文中，我们考虑弱安全 SMDC，其中在每个单独的消息上注入安全约束，并提供叠加编码是和率最优的条件的完整特征。提出了两种联合编码策略，与叠加编码相比，可以节省速率，其中一个消息的某些编码组件可以用作另一消息的加密密钥。通过应用汉不等式的不同变体，我们表明缺乏应用这两种编码策略的机会直接意味着叠加编码的最优性。进一步表明，在一组特定的安全约束下，所提出的联合编码策略之一可以用于构造实现最佳速率区域的代码。
Multilevel diversity coding is a classical coding model where multiple mutually independent information messages are encoded, such that different reliability requirements can be afforded to different messages. It is well known that superposition coding, namely separately encoding the independent messages, is optimal for symmetric multilevel diversity coding (SMDC) (Yeung-Zhang 1999). In the current paper, we consider weakly secure SMDC where security constraints are injected on each individual message, and provide a complete characterization of the conditions under which superposition coding is sum-rate optimal. Two joint coding strategies, which lead to rate savings compared to superposition coding, are proposed, where some coding components for one message can be used as the encryption key for another. By applying different variants of Han’s inequality, we show that the lack of opportunity to apply these two coding strategies directly implies the optimality of superposition coding. It is further shown that under a set of particular security constraints, one of the proposed joint coding strategies can be used to construct a code that achieves the optimal rate region.