Linear Network Coding Capacity Region of The Smart Repeater with Broadcast Erasure Channels
Abstract
This work considers the smart repeater network where a single source s wants to send two independent packet streams to destinations \d1,d2\ with the help of relay r. The transmission from s or r is modeled by packet erasure channels: For each time slot, a packet transmitted by s may be received, with some probabilities, by a random subset of \d1,d2,r\; and those transmitted by r will be received by a random subset of \d1,d2\. Interference is avoided by allowing at most one of \s,r\ to transmit in each time slot. One example of this model is any cellular network that supports two cell-edge users when a relay in the middle uses the same downlink resources for throughput/safety enhancement. In this setting, we study the capacity region of (R1,R2) when allowing linear network coding (LNC). The proposed LNC inner bound introduces more advanced packing-mixing operations other than the previously well-known butterfly-style XOR operation on overheard packets of two co-existing flows. A new LNC outer bound is derived by exploring the inherent algebraic structure of the LNC problem. Numerical results show that, with more than 85% of the experiments, the relative sum-rate gap between the proposed outer and inner bounds is smaller than 0.08% under the strong-relaying setting and 0.04% under arbitrary distributions, thus effectively bracketing the LNC capacity of the smart repeater problem.