TY - GEN

T1 - Constant-rate coding for multiparty interactive communication is impossible

AU - Braverman, Mark

AU - Efremenko, Klim

AU - Gelles, Ran

AU - Haeupler, Bernhard

PY - 2016/6/19

Y1 - 2016/6/19

N2 - We study coding schemes for multiparty interactive communication over synchronous networks that suffer from stochastic noise, where each bit is independently flipped with probability e. 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 1 994 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.

AB - We study coding schemes for multiparty interactive communication over synchronous networks that suffer from stochastic noise, where each bit is independently flipped with probability e. 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 1 994 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.

KW - Coding theory

KW - Communication complexity

KW - Interactive communication

KW - Network topology

KW - Rate

KW - Stochastic noise

UR - http://www.scopus.com/inward/record.url?scp=84979209094&partnerID=8YFLogxK

U2 - 10.1145/2897518.2897563

DO - 10.1145/2897518.2897563

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AN - SCOPUS:84979209094

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 999

EP - 1010

BT - STOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing

A2 - Mansour, Yishay

A2 - Wichs, Daniel

PB - Association for Computing Machinery

T2 - 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016

Y2 - 19 June 2016 through 21 June 2016

ER -