Strong Secrecy of Arbitrarily Varying Wiretap Channel With Constraints

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 Csiszar'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.