How Does Repetition Coding Enable Reliable and Covert Communications?

This letter tackles whether and how repetition coding enables reliable and covert communications by considering binary phase shift keying. Communication reliability and covertness are analyzed in terms of the bit error rate <inline-formula> <tex-math notation="LaTeX">$P_{e}$ </tex-math></inline-formula> and the minimum detection error probability <inline-formula> <tex-math notation="LaTeX">$\xi ^{\ast }$ </tex-math></inline-formula>. Our examination shows that, when a warden Willie knows the codeword structure, both <inline-formula> <tex-math notation="LaTeX">$P_{e}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\xi ^{\ast }$ </tex-math></inline-formula> are determined by the total power nP and do not depend on the codeword length <inline-formula> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula> or the transmit power <inline-formula> <tex-math notation="LaTeX">${P}$ </tex-math></inline-formula> individually. However, this conclusion does not hold for the unknown codeword structure, where increasing <inline-formula> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula> can significantly improve the communication reliability under the same covertness constraint, and vice versa.