Compute-and-Forward for Random-Access: The Case of Multiple Access Points

Compute-and-forward (C&F) recently finds new applications in random-access networks focusing on the single access point (AP) scenario. In this paper, we extend the use of C&F from the single AP scenario to the multi-AP scenario. To achieve this, we identify two major challenges and propose two novel solutions. First, we introduce an AP cooperation problem and develop an efficient distributed algorithm. Second, we introduce a joint channel estimation and active user recovery problem and propose a solution based on spare recovery techniques. In addition, we provide accurate throughput and delay expressions for C&F-based carrier-sense multiple access (CSMA) protocols. These expressions, together with our trace-driven simulations, demonstrate the significant advantages of C&F-based CSMA over conventional CSMA in the multi-AP scenario.

[1]  Bobak Nazer Successive compute-and-forward , 2012 .

[2]  Michael Gastpar,et al.  Compute-and-Forward: Harnessing Interference Through Structured Codes , 2009, IEEE Transactions on Information Theory.

[3]  Sae-Young Chung,et al.  Noisy network coding , 2010 .

[4]  T. Moon Error Correction Coding: Mathematical Methods and Algorithms , 2005 .

[5]  Soung Chang Liew,et al.  Hot topic: physical-layer network coding , 2006, MobiCom '06.

[6]  Dina Katabi,et al.  Zigzag decoding: combating hidden terminals in wireless networks , 2008, SIGCOMM '08.

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

[8]  Urs Niesen,et al.  Computation Alignment: Capacity Approximation Without Noise Accumulation , 2011, IEEE Transactions on Information Theory.

[9]  N. J. A. Sloane,et al.  Sphere Packings, Lattices and Groups , 1987, Grundlehren der mathematischen Wissenschaften.

[10]  Shlomo Shamai,et al.  On the capacity of cloud radio access networks with oblivious relaying , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).

[11]  Yonina C. Eldar,et al.  Compressive Link Acquisition in Multiuser Communications , 2012, IEEE Transactions on Signal Processing.

[12]  Young-Han Kim,et al.  On the capacity of cloud radio access networks , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).

[13]  Chen Feng,et al.  Performance Analysis of CSMA With Multi-Packet Reception: The Inhomogeneous Case , 2017, IEEE Transactions on Communications.

[14]  Alexander Sprintson,et al.  Joint Physical Layer Coding and Network Coding for Bidirectional Relaying , 2008, IEEE Transactions on Information Theory.

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

[16]  Wen Chen,et al.  Compute-and-Forward Network Coding Design over Multi-Source Multi-Relay Channels , 2012, IEEE Transactions on Wireless Communications.

[17]  Frank R. Kschischang,et al.  Slotted ALOHA with compute-and-forward , 2015, 2015 IEEE International Symposium on Information Theory (ISIT).

[18]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[19]  Wei Yu,et al.  Optimized Backhaul Compression for Uplink Cloud Radio Access Network , 2013, IEEE Journal on Selected Areas in Communications.

[20]  Michael Gastpar,et al.  Reliable Physical Layer Network Coding , 2011, Proceedings of the IEEE.

[21]  David Tse,et al.  Fundamentals of Wireless Communication , 2005 .

[22]  A. Robert Calderbank,et al.  A fast reconstruction algorithm for deterministic compressive sensing using second order reed-muller codes , 2008, 2008 42nd Annual Conference on Information Sciences and Systems.

[23]  Pedro M. Crespo,et al.  A novel scheme inspired by the compute-and-forward relaying strategy for the multiple access relay channel , 2019, Wirel. Networks.

[24]  Giuseppe Caire,et al.  Expanding the Compute-and-Forward Framework: Unequal Powers, Signal Levels, and Multiple Linear Combinations , 2015, IEEE Transactions on Information Theory.

[25]  Michael Gastpar,et al.  Cooperative strategies and capacity theorems for relay networks , 2005, IEEE Transactions on Information Theory.

[26]  Seyed Shwan Ashrafi Random Access over Multi-Packet Reception Channels: A Mean-Field Approach , 2016 .

[27]  Inaki Estella Aguerri,et al.  Lossy Compression for Compute-and-Forward in Limited Backhaul Uplink Multicell Processing , 2016, IEEE Transactions on Communications.

[28]  Damien Stehlé,et al.  Low-Dimensional Lattice Basis Reduction Revisited , 2004, ANTS.

[29]  Uri Erez,et al.  The Approximate Sum Capacity of the Symmetric Gaussian $K$ -User Interference Channel , 2012, IEEE Transactions on Information Theory.

[30]  David Wetherall,et al.  Taking the sting out of carrier sense: interference cancellation for wireless LANs , 2008, MobiCom '08.

[31]  A. Robert Calderbank,et al.  List decoding of noisy Reed-Muller-like codes , 2006, ArXiv.

[32]  Shengli Zhou,et al.  Application of compressive sensing to sparse channel estimation , 2010, IEEE Communications Magazine.

[33]  Uri Erez,et al.  The Approximate Sum Capacity of the Symmetric Gaussian $K$ -User Interference Channel , 2014, IEEE Trans. Inf. Theory.

[34]  Luc Vandendorpe,et al.  Compute-and-Forward on a Multiaccess Relay Channel: Coding and Symmetric-Rate Optimization , 2012, IEEE Transactions on Wireless Communications.

[35]  Frank R. Kschischang,et al.  An Algebraic Approach to Physical-Layer Network Coding , 2010, IEEE Transactions on Information Theory.