Secrecy coding for the binary multiplying wiretap channel

This paper studies the secure communication over Blackwell's binary multiplying channel (BMC) in the presence of an external eavesdropper, who has the same observation as the legitimate users. Based on the idea of Schalkwijk's coding scheme, we propose a secrecy coding scheme, aiming for both high efficiency (measured by the transmission sum-rate) and high secrecy (measured by the normalized equivocation at the eavesdropper). Moreover, we derive an achievable rate equivocation region for the general two-way wiretap channel. It is known that Schalkwijk's coding scheme achieves a transmission rate pair beyond Shannon's inner bound. Schalkwijk's coding scheme inherently provides some level of secrecy, which is further improved by randomizing the transmissions in our coding scheme. The numerical results show that both Schalkwijk's and our secrecy coding scheme can go beyond the proposed achievable sum-rate equivocation region. In general, our secrecy coding scheme outperforms Schalkwijk's coding scheme in terms of secrecy. Especially for a certain high sum-rate region, our secrecy coding scheme can achieve better secrecy than the proposed bound.