Choir codes: Coding for full duplex interference management

Communication networks conventionally operate with half-duplex methods and interference avoiding schemes to manage multiple transceivers. Here we consider a method in which nodes transmit and receive in concert to achieve full duplex communication without transmitter coordination. We build on a recent framework for full-duplex communication in ad-hoc wireless networks recently proposed by Zhang, Luo and Guo. An individual node in the wireless network either transmits or it listens to transmissions from other nodes but it cannot do both at the same time. There might be as many nodes as there are MAC addresses but we assume that only a small subset of nodes contribute to the superposition received at any given node in the network. We develop deterministic algebraic coding methods that allow simultaneous communication across the entire network. We call such codes choir codes. Users are assigned subspaces of F2m to define their transmit and listen times. Codewords on these subspaces are designed and proven to adhere to bounds on worst-case coherence and the associated matrix spectral norm. This in turn provides guarantees for multi-user detection using convex optimization. Further, we show that matrices for each receiver's listening times can be related by permutations, thus guaranteeing fairness between receivers. Compared with earlier work using random codes, our methods have significant improvements including reduced decoding/detection error and non-asymptotic results. Simulation results verify that, as a method to manage interference, our scheme has significant advantages over seeking to eliminate or align interference through extensive exchange of fine-grained channel state information.

[1]  Terence Tao,et al.  The Dantzig selector: Statistical estimation when P is much larger than n , 2005, math/0506081.

[2]  R. Calderbank,et al.  Chirp sensing codes: Deterministic compressed sensing measurements for fast recovery , 2009 .

[3]  E. Candès,et al.  Near-ideal model selection by ℓ1 minimization , 2008, 0801.0345.

[4]  Lei Zhang,et al.  Wireless peer-to-peer mutual broadcast via sparse recovery , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[5]  Stephen J. Wright,et al.  Sparse Reconstruction by Separable Approximation , 2008, IEEE Transactions on Signal Processing.

[6]  R. Varga Geršgorin And His Circles , 2004 .

[7]  Sundeep Rangan,et al.  On-Off Random Access Channels: A Compressed Sensing Framework , 2009, ArXiv.

[8]  R. McEliece Finite Fields for Computer Scientists and Engineers , 1986 .

[9]  A. Robert Calderbank,et al.  Sparse reconstruction via the Reed-Muller Sieve , 2010, 2010 IEEE International Symposium on Information Theory.

[10]  A. Robert Calderbank,et al.  Why Gabor frames? Two fundamental measures of coherence and their role in model selection , 2010, Journal of Communications and Networks.

[11]  Lei Zhang,et al.  Compressed Neighbor Discovery for Wireless Networks , 2010, ArXiv.

[12]  A. Robert Calderbank,et al.  Asynchronous code-division random access using convex optimization , 2011, Phys. Commun..

[13]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[14]  Lei Zhang,et al.  Virtual full-duplex wireless communication via rapid on-off-division duplex , 2010, 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton).