A scalable wireless communication architecture for average consensus

This paper introduces a multiple-access coding technique that is tailored to solve average consensus problems efficiently in wireless networks. We propose a novel data driven architecture which grants channel access to nodes based on their local data values. We analyze the performance of the scheme in the presence of quantization errors and noise. We show that our scheme is unbiased with respect to quantized consensus algorithms, it achieves good MSE performance, and it can be configured to provide a speedup in the convergence rate. The amount of speedup achieved is a function of |Qk| which indicates the number of quantization bins used to represent the state variables exchanged during the computation.

[1]  Arndt Bode Load balancing in distributed memory multiprocessors , 1991, [1991] Proceedings, Advanced Computer Technology, Reliable Systems and Applications.

[2]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[3]  Anna Scaglione,et al.  A simple method to reach detection consensus in massively distributed sensor networks , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[4]  R. Murray,et al.  Agreement problems in networks with directed graphs and switching topology , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[5]  R. Olfati-Saber,et al.  Distributed Kalman Filter with Embedded Consensus Filters , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[6]  Stephen P. Boyd,et al.  Distributed average consensus with least-mean-square deviation , 2007, J. Parallel Distributed Comput..

[7]  George Cybenko,et al.  Dynamic Load Balancing for Distributed Memory Multiprocessors , 1989, J. Parallel Distributed Comput..

[8]  A. Dimakis,et al.  Geographic gossip: efficient aggregation for sensor networks , 2006, 2006 5th International Conference on Information Processing in Sensor Networks.

[9]  Ke Liu,et al.  Type-Based Decentralized Detection in Wireless Sensor Networks , 2007, IEEE Transactions on Signal Processing.

[10]  Robert M. Gray,et al.  Toeplitz and Circulant Matrices: A Review , 2005, Found. Trends Commun. Inf. Theory.

[11]  Lang Tong,et al.  Type based estimation over multiaccess channels , 2006, IEEE Transactions on Signal Processing.

[12]  Stephen P. Boyd,et al.  A scheme for robust distributed sensor fusion based on average consensus , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[13]  Stephen P. Boyd,et al.  Gossip algorithms: design, analysis and applications , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[14]  Anna Scaglione,et al.  Opportunistic large arrays: cooperative transmission in wireless multihop ad hoc networks to reach far distances , 2003, IEEE Trans. Signal Process..

[15]  Stephen P. Boyd,et al.  Fast linear iterations for distributed averaging , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[16]  Panganamala Ramana Kumar,et al.  Computing and communicating functions over sensor networks , 2005, IEEE Journal on Selected Areas in Communications.

[17]  Anna Scaglione,et al.  On the wireless communication architecture for consensus problems , 2007 .

[18]  A. Scaglione,et al.  Differential Nested Lattice Encoding for Consensus Problems , 2007, 2007 6th International Symposium on Information Processing in Sensor Networks.

[19]  John N. Tsitsiklis,et al.  Problems in decentralized decision making and computation , 1984 .