Protecting Single-Hop Radio Networks from Message Drops

Single-hop radio networks (SHRN) are a well studied abstraction of communication over a wireless channel. In this model, in every round, each of the n participating parties may decide to broadcast a message to all the others, potentially causing collisions. We consider the SHRN model in the presence of stochastic message drops (i.e., erasures ), where in every round, the message received by each party is erased (replaced by ⊥ ) with some small constant probability, independently. Our main result is a constant rate coding scheme , allowing one to run protocols designed to work over the (noiseless) SHRN model over the SHRN model with erasures. Our scheme converts any protocol Π of length at most exponential in n over the SHRN model to a protocol Π ′ that is resilient to constant fraction of erasures and has length linear in the length of Π. We mention that for the special case where the protocol Π is non-adaptive , i.e., the order of communication is fixed in advance, such a scheme was known. Nevertheless, adaptivity is widely used and is known to hugely boost the power of wireless channels, which makes handling the general case of adaptive protocols Π both important and more challenging. Indeed, to the best of our knowledge, our result is the first constant rate scheme that converts adaptive protocols to noise resilient ones in any multi-party model.

[1]  Klim Efremenko,et al.  Tight Bounds for General Computation in Noisy Broadcast Networks , 2022, 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS).

[2]  Ran Gelles,et al.  Brief Announcement: Noisy Beeping Networks , 2020, PODC.

[3]  Klim Efremenko,et al.  Noisy Beeps , 2020, Electron. Colloquium Comput. Complex..

[4]  Klim Efremenko,et al.  Radio Network Coding Requires Logarithmic Overhead , 2019, 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS).

[5]  Ran Gelles,et al.  Constant-Rate Interactive Coding Is Impossible, Even in Constant-Degree Networks , 2019, IEEE Transactions on Information Theory.

[6]  Yael Tauman Kalai,et al.  Efficient Multiparty Interactive Coding for Insertions, Deletions, and Substitutions , 2019, PODC.

[7]  Klim Efremenko,et al.  Interactive coding over the noisy broadcast channel , 2018, Electron. Colloquium Comput. Complex..

[8]  Keren Censor-Hillel,et al.  Erasure Correction for Noisy Radio Networks , 2018, DISC.

[9]  Mark Braverman,et al.  Constant-Rate Coding for Multiparty Interactive Communication Is Impossible , 2017, J. ACM.

[10]  Keren Censor-Hillel,et al.  Broadcasting in Noisy Radio Networks , 2017, PODC.

[11]  Noga Alon,et al.  Reliable communication over highly connected noisy networks , 2016, Distributed Computing.

[12]  Yael Tauman Kalai,et al.  Interactive Coding for Multiparty Protocols , 2015, ITCS.

[13]  Leonard J. Schulman,et al.  The Adversarial Noise Threshold for Distributed Protocols , 2014, SODA.

[14]  Thomas M. Cover,et al.  Open Problems in Communication and Computation , 2011, Springer New York.

[15]  Eyal Kushilevitz,et al.  Computation in noisy radio networks , 2005, SODA '98.

[16]  Ilan Newman,et al.  Computing in fault tolerance broadcast networks , 2004, Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004..

[17]  Uriel Feige,et al.  Finding OR in a noisy broadcast network , 2000, Inf. Process. Lett..

[18]  Leonard J. Schulman,et al.  A coding theorem for distributed computation , 1994, STOC '94.

[19]  Leonard J. Schulman,et al.  Deterministic coding for interactive communication , 1993, STOC.

[20]  Leonard J. Schulman,et al.  Communication on noisy channels: a coding theorem for computation , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[21]  Robert G. Gallager,et al.  Finding parity in a simple broadcast network , 1988, IEEE Trans. Inf. Theory.

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

[23]  Klim Efremenko,et al.  Computation Over the Noisy Broadcast Channel with Malicious Parties , 2021, Electron. Colloquium Comput. Complex..

[24]  Sidhanth Mohanty,et al.  Algorithms for Noisy Broadcast with Erasures , 2018, ICALP.

[25]  Mark K. Singley,et al.  Adaptive Simulations , 2006, ICLS.

[26]  Navin Goyal,et al.  Lower bounds for the noisy broadcast problem , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[27]  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..