Wiretap channel II with a noisy main channel

In this paper, a wiretap channel where the transmitter and receiver communicate through a discrete memoryless channel, and the eavesdropper (Eve) has perfect access to a fixed fraction of transmitted symbols (of its choosing) is considered. An outer bound for the rate-equivocation region of the channel, for all such fractions, is derived. An achievable scheme, which provides an inner bound for the rate-equivocation region, is proposed. The achievability is established by defining a class of good codebooks for which there exists a good partition that achieves the required level of equivocation no matter what subset of symbols Eve chooses. It is shown that, for a uniform input distribution, the probability of this class of good codes approaches 1 as the block length increases. This generalizes the wiretap II model to one with a noisy main channel.