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This paper addresses the fundamental characteristics of information exchangevia multihop network coding over two-way relaying in a wireless ad hoc network.The end-to-end rate regions achieved by time-division multihop (TDMH),MAC-layer network coding (MLNC) and PHY-layer network coding (PLNC) are firstcharacterized. It is shown that MLNC does not always achieve better rates thanTDMH, time sharing between TDMH and MLNC is able to achieve a larger rateregion, and PLNC dominates the rate regions achieved by TDMH and MLNC. Anopportunistic scheduling algorithm for MLNC and PLNC is then proposed tostabilize the two-way relaying system for Poisson arrivals whenever the ratepair is within the Shannon rate regions of MLNC and PLNC. To understand thetwo-way transmission limits of multihop network coding, the sum-rateoptimization with or without certain traffic pattern and the end-to-enddiversity-multiplexing tradeoffs (DMTs) of two-way transmission over multiplerelay nodes are also analyzed.

Network Coding with Two-Way Relaying: Achievable Rate Regions and Diversity-Multiplexing Tradeoffs