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

This paper addresses the fundamental characteristics of information exchange via multihop network coding over two-way relaying in a wireless ad hoc network. The end-to-end rate regions achieved by timedivision multihop (TDMH), MAC-layer network coding (MLNC) and PHY-layer network coding (PLNC) are first characterized. It is shown that MLNC does not always achieve better rates than TDMH, time sharing between TDMH and MLNC is able to achieve a larger rate region, and PLNC dominates the rate regions achieved by TDMH and MLNC. An opportunistic scheduling algorithm for MLNC and PLNC is then proposed to stabilize the two-way relaying system for Poisson arrivals whenever the rate pair is within the Shannon rate regions of MLNC and PLNC. To understand the two-way transmission limits of multihop network coding, the sum-rate optimization with or without certain traffic pattern and the end-toend diversity-multiplexing tradeoffs (DMTs) of two-way transmission over multiple relay nodes are also analyzed. Index Terms Network Coding, Two-way Relaying, Achievable Rate, Opportunistic Scheduling and Diversity-Multiplexing Tradeoff. Liu and Andrews are with the Department of Electrical and Computer Engineering, the University of Texas at Austin, Austin TX 78712-0204, USA. Xue is with Intel Corp. at Santa Clara CA, USA. Parts of this work were presented at the IEEE International conference on communications, Beijing China, May 2008 and at the Allerton conference on communication, control and computing, IL USA, Sep. 2007. This work was supported in part by the National Science Council of Taiwan, R.O.C. under Contract TMS-941A-050. The contact author is J. G. Andrews (Email: [email protected]). Manuscript date: February 13, 2009.