Two-Flow Capacity Region of the COPE Principle for Wireless Butterfly Networks With Broadcast Erasure Channels

This paper characterizes the full capacity region of the COPE principle for 2-flow wireless butterfly networks with broadcast packet erasure channels (PECs). The capacity results in this paper allow for random overhearing with arbitrary overhearing probabilities, arbitrary scheduling policies, network-wide channel state information (CSI) feedback after each transmission, and potential use of nonlinear network codes. An information-theoretic outer bound is derived that takes into account the delayed CSI feedback of the underlying broadcast packet erasure channels. For the achievability, this paper proposes a new class of linear network codes, named as the space-based linear network coding (SBLNC), that achieves the capacity outer bound. Further, the proposed outer and inner bounds are later generalized for the setting in which a transmission may be heard by its 2-hop neighbor(s), the so-called opportunistic routing scenario. When allowing the possibility of opportunistic routing, the proposed inner and outer bounds do not always meet. Numerical experiments, however, show that the relative gap of the two bounds is less than 0.08% in average. The proposed bounds thus tightly bracket the capacity region even when combining the COPE principle with opportunistic routing.