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arXiv 0910.2502cs.ITmath.IT
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强保密干扰信道

Interference Channels with Strong Secrecy

Xiang He, Aylin Yener

摘要:

已知给定来自相同嵌套格码本的两个独立均匀分布的格点的实和,窃听者可以获得关于格点之一的值的每个信道至多1比特的信息。在这项工作中,我们研究了这1位信息对三种常用信息理论测量中表达的含糊度的影响,即,Shannon熵Renyi熵和最小熵然后,我们展示了它的应用程序中的干扰信道的机密消息。在我们以前的工作中,我们表明,嵌套格码可以优于高斯码在此信道下实现的速率与弱保密概念测量。在这里,与Renyi熵和最小熵测度,我们证明了同样的安全自由度是可以实现的强保密性的概念。新的编码方案的一个主要优点是,强保密性是从一个单一的格点,而不是一个序列的格点。因此,机密消息和窃听者的观察之间的互信息随着信道使用的数量的减少比先前已知的用于嵌套格码的强保密编码方法快得多。

英文摘要:

It is known that given the real sum of two independent uniformly distributed lattice points from the same nested lattice codebook, the eavesdropper can obtain at most 1 bit of information per channel regarding the value of one of the lattice points. In this work, we study the effect of this 1 bit information on the equivocation expressed in three commonly used information theoretic measures, i.e., the Shannon entropy, the Renyi entropy and the min entropy. We then demonstrate its applications in an interference channel with a confidential message. In our previous work, we showed that nested lattice codes can outperform Gaussian codes for this channel when the achieved rate is measured with the weak secrecy notion. Here, with the Renyi entropy and the min entropy measure, we prove that the same secure degree of freedom is achievable with the strong secrecy notion as well. A major benefit of the new coding scheme is that the strong secrecy is generated from a single lattice point instead of a sequence of lattice points. Hence the mutual information between the confidential message and the observation of the eavesdropper decreases much faster with the number of channel uses than previously known strong secrecy coding methods for nested lattice codes.

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