A Code and Rate Equivalence Between Secure Network and Index Coding
A Code and Rate Equivalence Between Secure Network and Index Coding
复制标题
DOI：
10.1109/jsait.2021.3054847
复制
发表时间：
2021-03
期刊：
影响因子：
--
通讯作者：
L. Ong;Badri N. Vellambi;J. Kliewer;Phee Lep Yeoh
中科院分区：
文献类型：
--
作者：
L. Ong;Badri N. Vellambi;J. Kliewer;Phee Lep Yeoh
建立索引编码和网络编码之间的代码等价性为代码设计提供了重要的见解。以前的作品显示了任何索引编码实例和网络编码实例之间的等价关系，其中一个实例的代码可以被翻译为具有相同解码错误性能的另一个实例的代码。等价性还显示了一个令人惊讶的结果，即任何网络编码实例都可以通过适当设计的代码转换映射到索引编码实例。在这篇文章中，我们将现有的等价性（实例映射和代码翻译）扩展到安全索引编码和安全网络编码之间的等价性，其中窃听者存在于网络中。在安全设置中，除了解码错误性能之外，任何代码构造都需要保证安全约束。这两个问题之间的速率等价也成立。
Establishing code equivalences between index coding and network coding provides important insights for code design. Previous works showed an equivalence relation between any index-coding instance and a network-coding instance, for which a code for one instance can be translated to a code for the other instance with the same decoding-error performance. The equivalence also showed a surprising result that any network-coding instance can be mapped to an index-coding instance with a properly designed code translation. In this article, we extend the existing equivalence (instance map and code translation) to one between secure index coding and secure network coding, where eavesdroppers are present in the network. In the secure setting, any code construction needs to guarantee security constraints in addition to decoding-error performance. A rate equivalence between these two problems is also established.