Linear Network Coding Capacity Region of The Smart Repeater with Broadcast Erasure Channels

This work considers the smart repeater network where a single source $s$ wants to send two independent packet streams to destinations $\{d_1,d_2\}$ 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 $\{d_1,d_2,r\}$; and those transmitted by $r$ will be received by a random subset of $\{d_1,d_2\}$. 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 $(R_1,R_2)$ 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.Comment: 24 pages, 4 figures, extended version for ISIT'1

Capacity and Algorithms for a Cognitive Network with Primary-Secondary User Cooperation

In this work, we examine cognitive radio networks, where secondary users may act as relays for messages sent by the primary user, hence offering performance improvement of primary transmissions, while at the same time obtaining more transmission opportunities for their own data. In particular, assuming the broadcast packet erasure model with feedback, we investigate the capacity of the fundamental cooperative cognitive radio network which consists of one primary and one secondary transmitter-receiver pairs. The primary transmitter is the owner of the channel and as such, we intend to keep its operations simple and to avoid increasing its storage requirements. Specifically, the primary transmitter does not receive data sent by the secondary transmitter and does not perform any coding operations. On the other hand, the secondary transmitter can overhear primary transmissions and is allowed to perform any coding operations. We develop an outer bound to the capacity of the fundamental cooperative cognitive radio network under consideration. Then, we propose a coding-scheduling algorithm suitable for this type of networks, which involves only XOR network coding operations. The complexity of the scheduling decisions of the proposed algorithm depends on the channel statistical parameters and three cases, depending on the relations between channel erasure probabilities, are distinguished. For the first two cases the rate region of the proposed algorithm coincides with the developed capacity outer bound, hence the algorithm is capacity achieving. For the third case, the rate region of the proposed algorithm is not identical to the outer bound; however, numerical results show that it is fairly close to the derived outer bound for a wide range of the statistical parameters of the system