On the Secondary Capacity of the Communication Protocols

In this paper we consider secondary communication channels, defined via utilization of the protocol overhead information in legacy communication systems, here referred to as primary systems. The secondary communication is carried out by rearranging the order of the packets which are put forward for transmission by the primary system. To motivate the models, we provide several scenarios with wireless primary communication systems. The secondary communication can be seen as a special case of cognitive radio, since additional information is sent by using the same spectrum as the primary system and without affecting the performance of the primary system. The primary system is frame-based and it determines a set of packets that need to be delivered within a frame. The arrangements of the packets within the frame is irrelevant for the primary system and that is creating the opportunity for secondary communication. We define two generic communication models, the permutation model and the combinatorial model, respectively. For both models, we define suitable discrete communication channels, where the error models are obtained by suitably transforming the packet erasures in the primary system. The capacity of these channels is analyzed. It turns out that the capacity results for the combinatorial communication model are related to the fundamental result by Shannon regarding channels with causal side information at the transmitter. The ideas presented in this paper set several interesting directions for future work.