Covert and Reliable Short-Packet Communications against A Proactive Warder

Wireless short-packet communications pose challenges to the security and reliability of the transmission. Besides, the proactive warder compounds these challenges, who detects and interferes with the potential transmission. An extra jamming channel is introduced by the proactive warder compared with the passive one, resulting in the inapplicability of analytical methods and results in exsiting works. Thus, effective system design schemes are required for short-packet communications against the proactive warder. To address this issue, we consider the analysis and design of covert and reliable transmissions for above systems. Specifically, to investigate the reliable and covert performance of the system, detection error probability at the warder and decoding error probability at the receiver are derived, which is affected by both the transmit power and the jamming power. Furthermore, to maximize the effective throughput, an optimization framework is proposed under reliability and covertness constraints. Numerical results verify the accuracy of analytical results and the feasibility of the optimization framework. It is shown that the tradeoff between transmission reliability and covertness is changed by the proactive warder compared with the passive one. Besides, it is shown that longer blocklength is always beneficial to improve the throughput for systems with optimized transmission rates. But when transmission rates are fixed, the blocklength should be carefully designed since the maximum one is not optimal in this case.