Broadcasting in Noisy Radio Networks

The widely-studied radio network model [Chlamtac and Kutten, 1985] is a graph-based description that captures the inherent impact of collisions in wireless communication. In this model, the strong assumption is made that node v receives a message from a neighbor if and only if exactly one of its neighbors broadcasts. We relax this assumption by introducing a new noisy radio network model in which random faults occur at senders or receivers. Specifically, for a constant noise parameter p ∈ [0, 1), either every sender has probability p of transmitting noise or every receiver of a single transmission in its neighborhood has probability p of receiving noise. We first study single-message broadcast algorithms in noisy radio networks and show that the Decay algorithm [Bar-Yehuda et al., 1992] remains robust in the noisy model while the diameter-linear algorithm of Gasieniec et al., 2007 does not. We give a modified version of the algorithm of Gasieniec et al., 2007 that is robust to sender and receiver faults, and extend both this modified algorithm and the Decay algorithm to robust multi-message broadcast algorithms, broadcasting Ω ( 1 log n log log n ) and Ω ( 1 log n ) messages per round, respectively. We next investigate the extent to which (network) coding improves throughput in noisy radio networks. In particular, we study the coding cap – the ratio of the throughput of coding to that of routing – in noisy radio networks. We address the previously perplexing result of Alon et al. 2014 that worst case coding throughput is no better than worst case routing throughput up to constants: we show that the worst case throughput performance of coding is, in fact, superior to that of routing – by a Θ(log(n)) gap – provided receiver faults are introduced. However, we show that sender faults have little effect on throughput. In particular, we show that any coding or routing scheme for the noiseless setting can be transformed to be robust to sender faults with only a constant throughput overhead. These transformations imply that the results of Alon et al., 2014 carry over to noisy radio networks with sender faults as well. As a result, if sender faults are introduced then there exist topologies for which there is a Θ(log logn) gap, but the worst case throughput across all topologies is Θ ( 1 log n ) for both coding and routing. ∗Supported in part by the Israel Science Foundation (grant 1696/14) and the Binational Science Foundation (grant 2015803). †Supported in part by the National Science Foundation through grants CCF-1527110 and CCF-1618280. ar X iv :1 70 5. 07 36 9v 1 [ cs .D C ] 2 1 M ay 2 01 7