We consider the problem of coding to ensure covert communication, which involves ensuring reliable communication between two legitimate parties while simultaneously guaranteeing a low probability of detection by an eavesdropper. Specifically, we develop an optimal low-complexity coding scheme that achieves the information-theoretic limits of covert communications over binary-input discrete memoryless channels (BI-DMCs). To justify our design, we first consider a regime in which information theory proves the possibility of covert communication without shared secret key and show the impossibility of achieving information-theoretic limits using linear codes without secret key. We then circumvent this impossibility by introducing non-linearity into the coding scheme through the use of pulse position modulation (PPM) and multilevel coding (MLC). This MLC-PPM scheme exhibits several appealing properties; in particular, for an appropriate decoder, the channel at a given level is independent of the total number of levels and the codeword length. We exploit these properties to show how one can use families of channel capacity- and channel resolvability-achieving codes to concretely instantiate a covert communication scheme.

中文翻译：

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二进制输入离散无记忆信道隐蔽通信的多级编码脉冲位置调制

我们考虑编码问题以确保隐蔽通信，这涉及确保两个合法方之间的可靠通信，同时保证被窃听者检测到的概率很低。具体来说，我们开发了一种最优的低复杂度编码方案，它实现了二进制输入离散无记忆通道 (BI-DMC) 上隐蔽通信的信息理论限制。为了证明我们的设计，我们首先考虑一种机制，其中信息理论证明了没有共享密钥的隐蔽通信的可能性，并表明使用没有密钥的线性代码实现信息理论限制是不可能的。然后，我们通过使用脉冲位置调制 (PPM) 和多级编码 (MLC) 将非线性引入编码方案，从而避免了这种可能性。这种 MLC-PPM 方案展示了几个吸引人的特性；特别是，对于合适的解码器，给定级别的信道与级别总数和码字长度无关。我们利用这些特性来展示如何使用一系列信道容量和信道可解析性实现代码来具体实例化隐蔽通信方案。