Communication for Generating Correlation: A Unifying Survey

Sudan, Madhu; Tyagi, Himanshu; Watanabe, Shun

doi:10.1109/tit.2019.2946364

Cited by 28 publications

(20 citation statements)

References 198 publications

(331 reference statements)

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“…For a source (X, Y ) ∼ µ, the r-round MIMK is the infimum of all C ≥ 0 such that there exists an r-round private-coin protocol Π such that IC int µ (Π) ≤ C and IC ext Theorem 4.1, we finally can state the single-letter characterization of achievable rates for r-round CRG. It is stated most precisely in[STW19], but similar results are shown in [LCV17, GJ18, Liu16, Ye05, GA10a, GA10b].…”

supporting

confidence: 77%

“…[STW19], Theorem III.2). For C ≥ 0, definẽC am-cr r (C) := sup Π=(Π 1 ,...,Πr):IC int µ (Π)≤C {IC ext µ (Π)} : C ≤ I r (X; Y )…”

mentioning

confidence: 95%

“…The case r = 1 of the next lemma, Lemma 5.6 was proven as part of the proof of Theorem 4.1 in [AC98]. It is also stated without proof in [STW19]. The proof will use the following elementary fact: the fact that Π = (Π 1 , .…”

mentioning

confidence: 96%

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Round Complexity of Common Randomness Generation: The Amortized Setting

Golowich¹,

Sudan²

2020

Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms

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In this work we study the effect of rounds of interaction on the common randomness generation (CRG) problem. In the CRG problem, two parties, Alice and Bob, receive samples X i and Y i , respectively, where (X i , Y i ) are drawn jointly from a source distribution µ. The two parties wish to agree on a common random key consisting of many bits of randomness, by exchanging messages that depend on each party's respective input and the previous messages. In this work we study the amortized version of the problem, i.e., the number of bits of communication needed per random bit output by Alice and Bob, in the limit as the number of bits generated tends to infinity. The amortized version of the CRG problem has been extensively studied in the information theory literature, though very little was known about the effect of interaction on this problem. Recently Bafna et al. (SODA 2019) considered the non-amortized version of the problem (so here the goal of the interaction is to generate a fixed number of random bits): they gave a family of sources µ r,n parameterized by r, n ∈ N, such that with r + 2 rounds of communication one can generate n bits of common randomness with this source with O(r log n) communication, whereas with roughly r/2 rounds the communication complexity is Ω(n/ poly log n). Note in particular that their source is designed with the target number of bits in mind and hence the result does not apply to the amortized setting.In this work we strengthen the work of Bafna et al. in two ways: First we show that the results extend to the classical amortized setting. We also reduce the gap between the round complexity in the upper and lower bounds to an additive constant. Specifically we show that for every pair r, n ∈ N the (amortized) communication complexity to generate Ω(n) bits of common randomness from the source µ r,n using r + 2 rounds of communication is O(r log n) whereas the amortized communication required to generate the same amount of randomness from r rounds is Ω( √ n). Our techniques exploit known connections between information complexity and CRG, and the main novelty is our ability to analyze the information complexity of protocols getting inputs from the source µ r,n .

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supporting

confidence: 77%

“…[STW19], Theorem III.2). For C ≥ 0, definẽC am-cr r (C) := sup Π=(Π 1 ,...,Πr):IC int µ (Π)≤C {IC ext µ (Π)} : C ≤ I r (X; Y )…”

mentioning

confidence: 95%

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Round Complexity of Common Randomness Generation: The Amortized Setting

Golowich¹,

Sudan²

2020

Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…In many models, one terminal corresponds to the sender station and the other corresponds to the receiver station. The availability of this CR allows to implement correlated random protocols leading to developing potentially faster and more efficient algorithms [1]. CR generation plays a major role in sequential secret key generation [2].…”

Section: Introductionmentioning

confidence: 99%

Common Randomness Generation over Slow Fading Channels

Ezzine¹,

Wiese²,

Deppe³

et al. 2021

Preprint

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This paper analyzes the problem of common randomness (CR) generation from correlated discrete sources aided by unidirectional communication over Single-Input Single-Output (SISO) slow fading channels with additive white Gaussian noise (AWGN) and arbitrary state distribution. Slow fading channels are practically relevant for wireless communications. We completely solve the SISO slow fading case by establishing its corresponding outage CR capacity using our characterization of its channel outage capacity. The generated CR could be exploited to improve the performance gain in the identification scheme. The latter is known to be more efficient than the classical transmission scheme in many new applications, which demand ultra-reliable low latency communication.

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“…Exact distributed sampling was studied by Anantharam and Borkar, [22], Kumar et al [23],Vellambi and Kliewer [24], [25]. See the survey by Sudan et al [26] for more details on communication for generating correlation. A weaker form of sampling which only requires joint typicality of the outputs has also been extensively investigated [7], [27]- [32] .…”

Section: Introductionmentioning

confidence: 99%

Coordination via Shared Randomness

Kurri

Prabhakaran

2019

2019 IEEE Information Theory Workshop (ITW)

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We study a distributed sampling problem where a set of processors want to output approximately (in the sense of asymptotically vanishing total variation distance) independent and identically distributed samples from a given joint distribution with the help of a coordinator. We consider two settings. In the omniscient coordinator setting, the coordinator has access to several independent sources of randomness and each processor has access to a subset of these sources. The oblivious coordinator setting is similar except that the coordinator does not have access to any of the shared randomness sources. In addition, all processors and the coordinator may privately randomize. In the omniscient coordinator setting, when the subsets at the processors are disjoint (individually shared randomness model), we characterize the rate of communication required from the coordinator to the processors over a multicast link. We also give an upper bound on the communication rate for the randomnesson-the-forehead model where each processor observes all but one source of randomness and we give an achievable strategy in the omniscient coordinator setting for the general case where the processors have access to arbitrary subsets of sources of randomness. Also, we consider a more general model where the processors observe components of correlated sources (with the coordinator observing all the components), where we characterize the communication rate when all the processors wish to output the same random sequence. In the oblivious coordinator setting, we completely characterize the trade-off region between the communication and shared randomness rates for the general case where the processors have access to arbitrary subsets of sources of randomness.

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Communication for Generating Correlation: A Unifying Survey

Cited by 28 publications

References 198 publications

Round Complexity of Common Randomness Generation: The Amortized Setting

Round Complexity of Common Randomness Generation: The Amortized Setting

Common Randomness Generation over Slow Fading Channels

Coordination via Shared Randomness

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