A Gale-Shapley algorithm for allocation of relayed parallel wiretap coding channels

Alice aims at transmitting Bob a message to be kept secret from Eve, with the assistance of relays operating in a decode-and-forward fashion. Each link between node couples comprises a set of parallel channels. Both Alice and relays knows all legitimate channel gains, while they only have a statistical knowledge of the channels to Eve. By fixing a secrecy outage probability per channel, we optimize power and rate of the messages sent by Alice to the relays (phase one) and from the relays to Bob (phase two), in order to maximize the achievable end-to-end outage secrecy rate. Since the phase-one rate cannot exceed the phase-two rate for each relay, the allocations in the two phases are tightly coupled, making the optimization quite challenging. Therefore we propose a solution based on the Gale-Shapley approach to the stable matching problem. The algorithm iterates between two stages, one in which each relay proposes Bob a secret rate on a specific channel, and another in which Bob discards the offer providing the lowest rate. The process is repeated until a single offer is available on each channel. Offers by the relays are based on (and in turns influence) the resource allocation by Alice with respect to her transmission to the relays. Numerical results are provided, showing the merit of the proposed solution with respect to existing approaches.