This paper considers the problem of covert communication with mismatched decoding, in which a sender wishes to reliably communicate with a receiver whose decoder is fixed and possibly sub-optimal, and simultaneously to ensure that the communication is covert with respect to a warden. We present single-letter lower and upper bounds on the information-theoretically optimal throughput as a function of the given decoding metric, channel laws, and the desired level of covertness. These bounds match for a variety of scenarios of interest, such as (i) when the channel between the sender and receiver is a binary-input binary-output channel, and (ii) when the decoding metric is particularized to the so-called erasures-only metric. The lower bound is obtained based on a modified random coding union bound with pulse position modulation (PPM) codebooks, coupled with a non-standard expurgation argument. The proof of the upper bound relies on a non-trivial combination of analytical techniques for the problems of covert communication and mismatched decoding.
翻译:本文审议了与不匹配解码的隐蔽通信问题,发送者希望与一个其解码器固定且可能是次最佳的接收器进行可靠通信,同时确保该通信与典狱长有关,我们根据特定解码指标、频道法和理想的隐蔽度水平,对信息-理论最佳传输方式提出单字母下限和上限,作为特定解码、频道法和理想的隐蔽度的函数。这些界限符合各种感兴趣的情况,例如(一) 发送者与接收者之间的渠道是二进二进制输出通道,以及(二) 解码指标是专门用于所谓的仅去除指标的。 下限依据一个经修改的随机编码结合,与脉动位置调制调(PPM)编码簿结合,加上非标准解码论证。上限的证据取决于对隐密通信和脱码问题的非三联的分析技术。