Constant-Rate Coding for Multiparty Interactive Communication Is Impossible

Braverman, Mark; Efremenko, Klim; Gelles, Ran; Haeupler, Bernhard

doi:10.1145/3050218

Cited by 13 publications

(2 citation statements)

References 39 publications

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“…Alon et al [ABE + 16] showed that if the topology is a clique, or a dense d-regular graph, then constant rate coding is also possible. Yet, Braverman, Efremenko, Gelles, and Haeupler [BEGH17] proved that a constant rate is impossible if the topology is a star. All the above works assume a synchronous fully-utilized network.…”

Section: Related Workmentioning

confidence: 99%

Efficient Multiparty Interactive Coding for Insertions, Deletions, and Substitutions

Gelles

Kalai

Ramnarayan

2019

Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing

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In the field of interactive coding, two or more parties wish to carry out a distributed computation over a communication network that may be noisy. The ultimate goal is to develop efficient coding schemes that can tolerate a high level of noise while increasing the communication by only a constant factor (i.e., constant rate).In this work we consider synchronous communication networks over an arbitrary topology, in the powerful adversarial insertion-deletion noise model. Namely, the noisy channel may adversarially alter the content of any transmitted symbol, as well as completely remove a transmitted symbol or inject a new symbol into the channel.We provide efficient, constant rate schemes that successfully conduct any computation with high probability as long as the adversary corrupts at most ε m fraction of the total communication, where m is the number of links in the network and ε is a small constant. This scheme assumes the parties share a random string to which the adversarial noise is oblivious. We can remove this assumption at the price of being resilient to ε m log m adversarial error. While previous work considered the insertion-deletion noise model in the two-party setting, to the best of our knowledge, our scheme is the first multiparty scheme that is resilient to insertions and deletions. Furthermore, our scheme is the first computationally efficient scheme in the multiparty setting that is resilient to adversarial noise.1 By "arbitrary" we mean that the topology of the network can be an arbitrary graph G = (V, E) where each node is a party and each edge is a communication channel connecting the parties associated with these nodes.2 That is, a channel that flips every bit with some constant probability ε ∈ (0, 1/2). 3 [JKL15] obtained this result for the specific star network, whereas [HS16] generalized this result to a network with arbitrary topology. 4 We assume that each insertion, deletion, or substitution counts as a single corruption.Theorem 1.2 (no common randomness, non-oblivious noise, informal). Let G = (V, E) be an arbitrary synchronous network with n = |V | nodes and m = |E| links. For any noiseless protocol Π over G with a predetermined order of speaking, and for any sufficiently small constant ε, there exists an efficient coding scheme that simulates Π over a noisy network G. The simulated protocol is robust to adversarial insertion, deletion, and substituition noise, assuming at most (ε/m log m)-fraction of the communication is corrupted. The simulated protocol communicates O(CC(Π)) bits, and succeeds with probability at least 1 − exp(−CC(Π)/m).In Appendix B we consider the case where the adversarial channel is non-oblivious, however, the parties pre-share randomness. In this case we show a coding scheme (Algorithm C) that is resilient to a somewhat higher noise level of ε/m log log m-fraction of insertion and deletion noise, while still incurring a constant blowup in the communication. See Appendix B for the complete details.3 Lemma 6.3. Let |Π| = CC(Π) 5m log(m) and let ε > 0 be a su...

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Section: Related Workmentioning

confidence: 99%

Efficient Multiparty Interactive Coding for Insertions, Deletions, and Substitutions

Gelles

Kalai

Ramnarayan

2019

Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing

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“…We devote Section 5 to sketch the proof of the more involved lower bound of Theorem 1.1. Full details can be found in the full version of this manuscript [6]. Below we give a rather intuitive overview of our lower bound result and the techniques we use.…”

Section: Theorem 12 (Upper Bound)mentioning

confidence: 99%

Constant-rate coding for multiparty interactive communication is impossible

Braverman

Efremenko

Gelles

et al. 2016

Proceedings of the Forty-Eighth Annual ACM Symposium on Theory of Computing

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We study coding schemes for multiparty interactive communication over synchronous networks that suffer from stochastic noise, where each bit is independently flipped with probability ε. We analyze the minimal overhead that must be added by the coding scheme in order to succeed in performing the computation despite the noise. Our main result is a lower bound on the communication of any noise-resilient protocol over a synchronous star network with n-parties (where all parties communicate in every round). Specifically, we show a task that can be solved by communicating T bits over the noise-free network, but for which any protocol with success probability of 1 − o(1) must communicate at least Ω(T log n log log n) bits when the channels are noisy. By a 1994 result of Rajagopalan and Schulman, the slowdown we prove is the highest one can obtain on any topology, up to a log log n factor. We complete our lower bound with a matching coding scheme that achieves the same overhead; thus, the capacity of (synchronous) star networks is Θ(log log n/ log n). Our bounds prove that, despite several previous coding schemes with rate Ω(1) for certain topologies, no coding scheme with constant rate Ω(1) exists for arbitrary n-party noisy networks.

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Making asynchronous distributed computations robust to noise

2018

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We consider the problem of making distributed computations robust to noise, in particular to worst-case (adversarial) corruptions of messages. We give a general distributed interactive coding scheme which simulates any asynchronous distributed protocol while tolerating an optimal corruption of a Θ(1/n) fraction of all messages while incurring a moderate blowup of O(n log 2 n) in the communication complexity.Our result is the first fully distributed interactive coding scheme in which the topology of the communication network is not known in advance. Prior work required either a coordinating node to be connected to all other nodes in the network or assumed a synchronous network in which all nodes already know the complete topology of the network.

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Constant-Rate Coding for Multiparty Interactive Communication Is Impossible

Cited by 13 publications

References 39 publications

Efficient Multiparty Interactive Coding for Insertions, Deletions, and Substitutions

Efficient Multiparty Interactive Coding for Insertions, Deletions, and Substitutions

Constant-rate coding for multiparty interactive communication is impossible

Making asynchronous distributed computations robust to noise

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