Stochastic Resonance and The Secrecy Capacity of Wiretap Channels

隆太郎 松本, Ryutaroh Matsumoto

Yiqi Chen, Dan Nong He, Chenhao Ying +1 more

The strong secrecy transmission problem of the arbitrarily varying wiretap channel (AVWC) with input and state constraints is investigated in this paper. First, a stochastic-encoder code lower bound of the strong secrecy capacity is established by applying the type argument and Csiszár’s almost independent coloring lemma. Then, a superposition stochastic-encoder code lower bound of the secrecy capacity is provided. The superposition stochastic-encoder code lower bound can be larger than the ordinary stochastic-encoder code lower bound. Random code lower and upper bounds of the secrecy capacity of the AVWC with constraints are further provided. Based on these results, we further consider a special case of the model, namely severely less noisy AVWC, and give the stochastic-encoder code and random code capacities. It is proved that the stochastic-encoder code capacity of the AVWC with constraints is either equal to or strictly smaller than the corresponding random code capacity, which is consistent with the property of the ordinary AVC. Finally, some numerical examples are presented to better illustrate our capacity results. Compared to the soft covering lemma that requires the codewords to be generated i.i.d., our method has more relaxed requirements regarding codebooks. It is proved that the good codebooks for secure transmission can be generated by choosing codewords randomly from a given type set, which is critical when considering the AVWC with constraints.

Igor Bjelaković, Holger Boche, Jochen Sommerfeld

Md. K. Hossan, Sanjay Karmakar, Anirban Ghosh

We consider the fast-fading Gaussian wiretap channel with single antenna nodes and without channel state information at the transmitter (CSIT), where the fading processes of the two links are arbitrary and independent of each other. We derive an upper bound to the secrecy capacity for this channel and an achievable rate as well. Subsequently, we identify a class of channel statistics for which the outer bound and the achievable rates are identical thereby characterizes the exact secrecy capacity of the channel. The class of channels with such channel statistics are called stochastically degraded in this paper. Many practical wireless settings including the Rayleigh fading environment fall under this stochastically degraded class. We illustrate our results by computing explicit expression for the secrecy capacity for Rayleigh distributed wiretap channels.

S. Leung-Yan-Cheong

Yogesh Sankarasubramaniam, Andrew Thangaraj, Kapali Viswanathan

Information-theoretic security offered by the wiretap channel model has been extensively studied for various scenarios recently. One scenario that has not received much attention is secrecy for systems with memory in the form of input constraints or inter-symbol interference (ISI). In this work, we consider finite state wiretap channels (FSWCs), which model the scenario of secrecy with memory. Using results on secrecy capacity for arbitrary wiretap channels, we first arrive at the secrecy capacity of a FSWC. Then, we develop a stochastic algorithm for computing tight lower bounds on the secrecy capacity of a less-noisy FSWC, and illustrate the computation through examples. Our results provide numerical comparisons between secrecy capacities with and without memory, and provide specific targets for code design.