Capacity Results for Arbitrarily Varying Wiretap Channels

Abstract: In this work the arbitrarily varying wiretap channel AVWC is studied. We derive a lower bound on the random code secrecy capacity for the average error criterion and the strong secrecy criterion in the case of a best channel to the eavesdropper by using Ahlswede's robustification technique for ordinary AVCs. We show that in the case of a non-symmetrisable channel to the legitimate receiver the deterministic code secrecy capacity equals the random code secrecy capacity, a result similar to Ahlswede's dichotomy result for ordinary AVCs. Using this we can derive that the lower bound is also valid for the deterministic code capacity of the AVWC. The proof of the dichotomy result is based on the elimination technique introduced by Ahlswede for ordinary AVCs. We further prove upper bounds on the deterministic code secrecy capacity in the general case, which results in a multi-letter expression for the secrecy capacity in the case of a best channel to the eavesdropper. Using techniques of Ahlswede, developed to guarantee the validity of a reliability criterion, the main contribution of this work is to integrate the strong secrecy criterion into these techniques.