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%, thus effectively bracketing the LNC capacity of the smart repeater problem.

This paper studies the capacity region when three nodes {1, 2,3} communicate with each other by sending packets through unreliable wireless medium. For each time slot, with some probabilities a packet sent by node i may be received by both of the other nodes j and k; received only by node j (or node k); or received by neither node. Interference is avoided by enforcing that at most one node can transmit in each time slot. We assume that node i can always reach node j, possibly with the help of the third node k, for any i ≠ j pairs (thus the term fully connected). One notable example of this model is any CSMA-based Wi-Fi network with three nodes within the hearing range of each other. We consider the most general traffic demands possible in this setting. Namely, there are six private-information flows with rates (R1→2, R1→3, R2→1, R2→3, R3→1, R3→2), respectively, and three common-information flows with rates (R1→23, R2→31, R3→12), respectively. We characterize the 9-dimensional Shannon capacity region within a gap that is inversely proportional to the packet size (bits). The gap can be attributed to exchanging reception status (ACK/NACK) and can be further reduced to zero if we allow such feedbacks to be transmitted via a separate control channel. For normal-sized packets, say 12000 bits, our results effectively characterize the capacity region for many important scenarios, e.g., wireless access-point networks with client-to-client cooperative communications, and wireless two-way relay networks with packet-level coding and processing. Technical contributions of this paper include a new converse for many-to-many network communications and a new capacity-approaching scheme based on simple linear network coding operations.

This work considers the fully-connected 3-node packet erasure network: For each time slot, with some probabilities a packet sent by any node i may be received by both of the other nodes j and k; received only by node j (or node k); or received by neither nodes. Interference is avoided by enforcing that at most one node can transmit in each time slot. We assume that node i can always reach node j, possibly with the help of the third node k, for any i ≠ j pairs (thus the term fully-connected). One example of this model is any Wi-Fi network with 3 nodes within the hearing range of each other. We consider the most general traffic demands. Namely, there are six private-information flows with rates (R1→2,R1→3,R2→1, R2→3,R3→1,R3→2), respectively, and three common-information flows with rates (R1→23,R2→31,R3→12), respectively. We characterize the 9-dimensional Shannon capacity region within a gap that is inversely proportional to the packet size (bits). The gap can be attributed to exchanging reception status (ACK) and can be further reduced to 0 if we allow ACK to be transmitted via a separate control channel. For normal-sized packets, say 12000 bits, our results have thus effectively characterized the capacity region. Technical contributions of this work include a new converse for many-to-many network communications and a new capacity-approaching simple linear network coding scheme.

This paper studies the capacity of the two-receiver multiple-input broadcast packet erasure channels (PECs) with channel output feedback, which is in contrast with the single-input setting of the existing works. Motivated by the immense success of linear network coding (LNC) in theory and in practice, this paper first focuses on LNC schemes and characterizes the LNC feedback capacity region of two-receiver multiple-input broadcast PECs. A new linear-space-based approach is proposed, which unifies the problems of finding a capacity outer bound and devising the achievability scheme into a single linear programming problem. In particular, an LP solver is used to exhaustively search for the LNC scheme(s) with the best possible throughput, the result of which is thus guaranteed to attain the LNC feedback capacity. It is then proven by pure algebraic arguments that the LNC capacity region matches a simple capacity region outer bound, which proves that the derived LNC capacity region is indeed the true capacity. A byproduct of the above results is a complete LNC capacity region characterization for two-receiver partially Markovian and partially controllable broadcast PECs.

Random linear network coding (RLNC) is widely used in practical network coding (NC) protocol design. Recent results show that RLNC also plays an important role in capacity-achieving intersession NC schemes for erasure-based 1-hop relay networks. This work quantifies the common information of RLNC over a 1-hop broadcast packet erasure channel. Several potential applications are discussed, including source coding, intersession NC, and broadcasting with common and private information.

This paper proposes a rate allocation scheme for throughput maximization considering rate fairness in wireless relay systems. The throughput maximization problem is formulated to two link data rate balancing problems: global balancing and local balancing. And the rate fairness is converted to data rate balancing of each destinations. Based on this, we construct a feasible rate region (FRR) which is the set of achievable data rates. Since FRR is a polyhedra, rate allocation is performed by searching the intersection points of FRR. In addition, if the system is infeasible, the proposed rate allocation removes the destination for system feasibility. Simulation results reveal that the proposed rate allocation maximizes the throughput with satisfying rate fairness, not only for the feasible case but also for the infeasible case.

In this paper, we propose an asymmetric diversity modulation (ADM) scheme for a single-source relay system that utilizes the relay's higher transmission ability as a form of diversity. To achieve this, the proposed method transmits multiple source bits over a high-order modulating relay as a way to provide additional time diversity. The spatial and time diversity then undergo 'bit'-based combining at the destination. Using the proposed 'bit'-based channel combining method, we derive the theoretical bit error rate (BER) for such a system. Moreover, we investigate the fact that the proposed scheme shows a performance trade-off between bit power and time diversity resulting from the reduced bit power caused by a high-order modulating relay.