Physical Layer Network Coding, Compute-and-Forward, Lattice Codes

One major challenge differentiating multi-user communications from its point-to-point counterpart is that in a multi-user scenario, signals from one node would cause interference to nodes within the transmission range. Recently, a novel perspective on dealing with interference has emerged. The main idea is to harness interference via structured codes (see the work of Nazer and Gastpar, Wilson et al, Ordentlich et al, Liew et al, Chung). The main idea behind such a paradigm is to enable the destination nodes (typically relay nodes in a larger network) to compute and forward functions of messages rather than decoding them individually. The chosen functions have to in some sense match the operation induced by the channel so that the structural gains offered by the channel can be exploited.

At the heart of this strategy lies codes constructed from lattices (or nested lattice codes of Erez and Zamir to be specific). We have been interested in seeking answers to many questions within this framework. The questions include - how can we construct lattice codes and decoders in a computationally efficient way to implement the compute-and-forward paradigm ? What kinds of functions can be computed at the relays and at what transmission rates? What happens in the presence of asynchronous transmission? What happens in the presence of fading?. Some of our findings have been published in the following papers.

• Y.-C. Huang and K.R. Narayanan, Construction $\pi_A$ and $\pi_D$ lattices : Construction, Goodness and Decoding Algorithms, submitted to the IEEE Transactions on Information Theory, July 2015, pdf
• Y.-C. Huang, K.R. Narayanan and T. Liu, Coding for Parallel Gaussian Bidirectional Channels: A Deterministic Approach, to appear in the IEEE Transactions on Information Theory, 2016
• E. Tunali, Y.-C. Huang, J. Boutros and K.R. Narayanan, Lattices over Eisenstein Integers for Compute-and-Forward", IEEE Transactions on Information Theory, pp. 5306-5321, Vol. 61, No. 10, October 2015
• P.-C. Wang, Y.-C. Huang, and K.R. Narayanan, Asynchronous Physical Layer Network Coding, IEEE Journal of Selected Areas in Communication, pp. 309-322, Vol. 33, No. 2, 2015
• A. Vem, Y.-C. Huang, K.R. Narayanan and H.D. Pfister, Multilevel Lattices based on Spatially-Coupled LDPC Codes with Applications, in proceedings of the IEEE International Symposium on Information Theory, pp. 2336-2340, July 2014
• B. Hern and K.R. Narayanan, Multilevel Coding Schemes for Compute-and-Forward with Flexible Decoding, IEEE Transactions on Information Theory, pp. 7613-7631, Vol. 59, No. 11, Nov. 2013
• Y.-C. Huang, N. E. Tunali and K.R. Narayanan, A Compute-and-Forward Scheme for Gaussian Bi-Directional Relaying with Inter-Symbol Interference, IEEE Transactions on Communications, pp. 1011-1019, Vol. 61, No. 3, March 2013
• A. Khisti, B. Hern and K.R. Narayanan, On Modulo-Sum Computation over an Erasure Multiple Access Channel, IEEE Transactions on Information Theory, pp. 4129-4138, Vol. 59, No. 7, Aug. 2013
• M. P. Wilson, K.R. Narayanan, H. Pfister and A. Sprintson, Joint Physical Layer and Network Coding for Bi-Directional Relaying, IEEE Transactions on Information Theory, pp. 5641-5654, Vol. 56, No. 11, November 2010, | pdf
page revision: 7, last edited: 06 Nov 2015 16:46