Broadcast Throughput in Radio Networks: Routing vs. Network Coding

The broadcast throughput in a network is defined as the average number of messages that can be transmitted per unit time from a given source to all other nodes when time goes to infinity. Classical broadcast algorithms treat messages as atomic tokens and route them from the source to the receivers by making intermediate nodes store and forward messages. The more recent network coding approach, in contrast, prompts intermediate nodes to mix and code together messages. It has been shown that certain wired networks have an asymptotic network coding gap, that is, they have asymptotically higher broadcast throughput when using network coding compared to routing. Whether such a gap exists for wireless networks has been an open question of great interest. We approach this question by studying the broadcast throughput of the radio network model which has been a standard mathematical model to study wireless communication. We show that there is a family of radio networks with a tight Θ(log log n) network coding gap, that is, networks in which the asymptotic throughput achievable via routing messages is a Θ(log log n) factor smaller than that of the optimal network coding algorithm. We also provide new tight upper and lower bounds showing that the asymptotic worst-case broadcast throughput over all networks with n nodes is Θ(1/log n) messages-per-round for both routing and network coding.

[1]  Fabian Kuhn,et al.  A New Perspective on Vertex Connectivity , 2013, SODA.

[2]  David Peleg,et al.  Time-Efficient Broadcasting in Radio Networks: A Review , 2007, ICDCIT.

[3]  Igor Potapov,et al.  Gossiping with Unit Messages in Known Radio Networks , 2002, IFIP TCS.

[4]  Eyal Kushilevitz,et al.  An Omega(D log (N/D)) Lower Bound for Broadcast in Radio Networks , 1998, SIAM J. Comput..

[5]  Dariusz R. Kowalski,et al.  Many-to-Many Communication in Radio Networks , 2007, Algorithmica.

[6]  Dariusz R. Kowalski,et al.  Average-Time Complexity of Gossiping in Radio Networks , 2006, SIROCCO.

[7]  Nancy A. Lynch,et al.  Broadcasting in unreliable radio networks , 2010, PODC.

[8]  Eyal Kushilevitz,et al.  Communication Complexity , 1997, Adv. Comput..

[9]  C. Fragouli,et al.  On the Benefits of Network Coding for Wireless Applications , 2006, 2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks.

[10]  Andrzej Pelc,et al.  Broadcasting in undirected ad hoc radio networks , 2003, PODC '03.

[11]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[12]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[13]  David Peleg,et al.  Faster communication in known topology radio networks , 2005, PODC '05.

[14]  Wojciech Rytter,et al.  Fast broadcasting and gossiping in radio networks , 2002, J. Algorithms.

[15]  Peter Sanders,et al.  Polynomial time algorithms for network information flow , 2003, SPAA '03.

[16]  Zongpeng Li,et al.  A Constant Bound on Throughput Improvement of Multicast Network Coding in Undirected Networks , 2009, IEEE Transactions on Information Theory.

[17]  Imrich Chlamtac,et al.  On Broadcasting in Radio Networks - Problem Analysis and Protocol Design , 1985, IEEE Transactions on Communications.

[18]  Qin Xin,et al.  Optimal Gossiping with Unit Size Messages in Known Topology Radio Networks , 2006, CAAN.

[19]  Noga Alon,et al.  A Lower Bound for Radio Broadcast , 1991, J. Comput. Syst. Sci..

[20]  Ashish Goel,et al.  On the Network Coding Advantage for Wireless Multicast in Euclidean Space , 2008, 2008 International Conference on Information Processing in Sensor Networks (ipsn 2008).

[21]  Muriel Médard,et al.  XORs in the Air: Practical Wireless Network Coding , 2006, IEEE/ACM Transactions on Networking.

[22]  Majid Khabbazian,et al.  Time-efficient randomized multiple-message broadcast in radio networks , 2011, PODC '11.

[23]  Aravind Srinivasan,et al.  Integrality ratio for group Steiner trees and directed steiner trees , 2003, SODA '03.

[24]  Rudolf Ahlswede,et al.  Network information flow , 2000, IEEE Trans. Inf. Theory.

[25]  Reuven Bar-Yehuda,et al.  On the Time-Complexity of Broadcast in Multi-hop Radio Networks: An Exponential Gap Between Determinism and Randomization , 1992, J. Comput. Syst. Sci..

[26]  Calvin C. Newport.  Brief announcement: a shorter and stronger proof of an Ω(d log(n/d)) lower bound for broadcast in radio networks , 2013, PODC '13.

[27]  Ding Liu,et al.  On Randomized Broadcasting and Gossiping in Radio Networks , 2002, COCOON.

[28]  Majid Khabbazian,et al.  A Bound on the Throughput of Radio Networks , 2013, ArXiv.

[29]  Eyal Kushilevitz,et al.  An Ω(D log(N/D)) lower bound for broadcast in radio networks , 1993, PODC '93.

[30]  Wojciech Rytter,et al.  A Randomized Algorithm for Gossiping in Radio Networks , 2001, COCOON.

[31]  Roger Wattenhofer,et al.  Local broadcasting in the physical interference model , 2008, DIALM-POMC '08.

[32]  Majid Khabbazian,et al.  Randomized broadcast in radio networks with collision detection , 2013, PODC '13.

[33]  Bernhard Haeupler,et al.  Analyzing Network Coding (Gossip) Made Easy , 2010, J. ACM.

[34]  Andrzej Pelc,et al.  Optimal Deterministic Broadcasting in Known Topology Radio Networks , 2006, Distributed Computing.

[35]  Nancy A. Lynch,et al.  Decomposing broadcast algorithms using abstract MAC layers , 2010, DIALM-POMC '10.

[36]  Wojciech Rytter,et al.  Broadcasting algorithms in radio networks with unknown topology , 2006, J. Algorithms.

[37]  Leszek Gasieniec,et al.  Faster Deterministic Gossiping in Directed Ad Hoc Radio Networks , 2004, SWAT.

[38]  Amit Agarwal,et al.  On the advantage of network coding for improving network throughput , 2004, ITW.

[39]  Nancy A. Lynch,et al.  Bounds on Contention Management in Radio Networks , 2012, DISC.

[40]  C. SIAMJ..  AN Ω(D log(N/D)) LOWER BOUND FOR BROADCAST IN RADIO NETWORKS∗ , 1998 .

[41]  Reuven Bar-Yehuda,et al.  Multiple Communication in Multihop Radio Networks , 1993, SIAM J. Comput..

[42]  Muriel Médard,et al.  Algebraic gossip: a network coding approach to optimal multiple rumor mongering , 2006, IEEE Transactions on Information Theory.

[43]  Andrzej Lingas,et al.  Gossiping with Bounded Size Messages in ad hoc Radio Networks , 2002, ICALP.

[44]  Dong Nguyen,et al.  Wireless Broadcast Using Network Coding , 2009, IEEE Transactions on Vehicular Technology.

[45]  Reuven Bar-Yehuda,et al.  Multiple communication in multi-hop radio networks , 1989, PODC '89.

[46]  M. Medard,et al.  On the multiple unicast network coding, conjecture , 2009, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton).