The Capacity-Equivocation Region Of Finite-state Markov Wiretap Channel

This paper is for the wiretap channel of non-DMC case, which is due to Wyner’sWire-Tap Channel [1] and Ozarow’s Wire-Tap Channel II [2]. K data bits are encodedinto N> K bits and transmitted to the receiver via a discrete memoryless channel(DMC). An intruder observes data from the receiver via a fnite-state Markov erasurechannel (FSMEC). Our goal is to design the encoder-decoder to maximize intruder’suncertainty about the sent data while the receiver can recover the sent K data bitsperfectly (i.e. the error rate tends to0). The encoder doesn’t know the specifc valueof channel state at each time index, but the probability distribution of channel state isavailable.The capacity region considering the transmission rate R, and equivocation d isgiven in this new model. Furthermore, the secrecy capacity, which provides the besttransmission rate with perfect secrecy, is formulated. To establish the capacity region,the concept of general erasure channel (GEC) is introduced. It is shown that FSMEC isa special case of GEC. The proof of direct part is based on Wyner’s idea in [1] exceptthat the codewords are partitioned into2NRbins randomly in [1], while we should fnda “good” partition in this paper. The concept of strong typicality is modifed to adaptto the new model.