Capacity region of two symmetric nearby erasure channels with channel state feedback

This work considers a commonly encountered wireless transmission scenario: Two nearby 1-hop flows s₁ → d₁ and s₂ → d₂ are within the transmission range of each other. The network nodes thus have to share the time resources, which limits the sum-rate performance. On the other hand, both s_i and d_i can (occasionally) overhear the transmission of the other pair (s_j, d_j) for all i ≠ j, which opens up the opportunity of using network coding (NC) and ACK/NACK to improve the throughput. The key challenge, however, is that any dedicated communication between s₁ and s₂ also consumes the precious time resources. Hence NC coordination must be achieved through unreliable overhearing. In this work, the above scenario is modeled as four wireless nodes interconnected by broadcast erasure channels with channel state feedback. The corresponding capacity region (R1,R2) is fully characterized for the setting of symmetric, spatially independent erasure channels.