Secure Multiplex Coding Attaining Channel Capacity in Wiretap Channels

It is known that a message can be transmitted safely against any wiretapper via a noisy channel without a secret key if the coding rate is less than the so-called secrecy capacity C
_S
, which is usually smaller than the channel capacity C. In order to remove the loss C-C
_S
, we propose a multiplex coding scheme with plural independent messages. In this paper, it is shown that the proposed multiplex coding scheme can attain the channel capacity as the total rate of the plural messages and the perfect secrecy for each massage. Several bounds of achievable multiplex coding rate region are derived for general wiretap channels in the sense of information-spectral methods, by extending Hayashi's proof, in which the coding of the channel resolvability is applied to wiretap channels. Furthermore, the exact region for deterministic coding is determined for stationary memoryless full-rank wiretap channels.