A novel scheduling algorithm for physical-layer network coding under Markov model in wireless multi-hop network q Zhaolong Ning, Qingyang Song ⇑ , Yao Yu College of Information Science and Engineering, Northeastern University, Shenyang 110819, China article info Article history: Available online 16 August 2012 abstract Physical-layer network coding (PNC) is a promising approach for wireless networks: it allows nodes to transmit simultaneously and encode packets by superposing signals at the physical layer, which can improve throughput. Because of the difficulty in scheduling simultaneous transmissions, we propose an opportunistic scheduling algorithm in the media access control (MAC) layer and analyze the achievable throughput of the Denoise-and-Forward (DF) PNC scheme for both symmetric and asymmetric channel statuses, where random errors may occur for both BPSK and QPSK modulation techniques. Simulation results show that our algorithm cannot only improve throughput but can also adapt to varying channel conditions. It is further revealed that for the same throughput, our algorithm is more power-efficient with an asymmetric channel status than with a symmet- ric channel status. Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved. 1. Introduction The shared wireless medium is the chief factor that limits the capacity of wireless multi-hop networks. Overlapped sig- nals in wireless communication systems have always been considered to be harmful [1,2]. However, the wireless broadcast medium enables enhanced interactions among wireless transreceivers, and the emergence of network coding has shifted the paradigm under which network communications are designed. In conventional network coding (CNC) schemes [3,4], a relay node encodes packets after receiving them in a separate communication phase, while in physical-layer network coding (PNC) [5–14], the relay node encodes packets during simultaneous transmissions. It is a simple fact in physics that when multiple electromagnetic (EM) waves come together within the same physical space, they can add. The mixing of EM waves is a form of network coding performed by nature [8]. The greatest difference between CNC and PNC is the coding pattern. In CNC, the relay node performs the XOR operation on bit streams within the network layer (or other, higher layers). In contrast, the encoding is processed within the physical layer in PNC. To demonstrate this difference, we first discuss a simple ‘‘Alice– Relay–Bob’’ model. As shown in Fig. 1, the goal of this three-node system is to exchange information between nodes A (Alice) and B (Bob) with the help of node R (Relay). In a traditional relaying scheme, four time slots are required to complete the transmissions. With the use of CNC, only three time slots are required for the exchange. Node A transmits X A to the relay node R in the first time slot, then node B sends X B to R in the second time slot. In the third time slot, node R broadcasts X R =X A  X B to nodes A and B, where  is the XOR operation. Because node A knows X A , message X B can be decoded from the received signal X R . Similarly, node B can decode X A with the a priori information of X B . Only two time slots are required in the PNC scheme, 0045-7906/$ - see front matter Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compeleceng.2012.07.017 q Reviews processed and recommended for publication to Editor-in-Chief by Associate Editor Dr. Paul Cotae. ⇑ Corresponding author. Address: College of Information Science and Engineering, Northeastern University, P.O. Box 365, Liaoning, Shenyang 110819, China. Tel./fax: +86 24 83684219. E-mail address: lilysong76@gmail.com (Q. Song). Computers and Electrical Engineering 39 (2013) 1625–1636 Contents lists available at SciVerse ScienceDirect Computers and Electrical Engineering journal homepage: www.elsevier.com/locate/compeleceng