Communication Requirements for Generating Correlated Random Variables

Paul Cuff (Stanford University)

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Communication Requirements for Generating Correlated Random Variables

Information Theory · Submitted 1 May 2008

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim This work characterizes the optimal tradeoff between the amount of common randomness used and the required rate of description.

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,541 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.12 · human participants 0.02 · controlled comparison 0.14 · randomized assignment 0.02 · states quantitative result 0.35 · compares with prior results 0.87 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Two familiar notions of correlation are rediscovered as extreme operating points for simulating a discrete memoryless channel, in which a channel output is generated based only on a description of the channel input. Wyner's "common information" coincides with the minimum description rate needed. However, when common randomness independent of the input is available, the necessary description rate reduces to Shannon's mutual information. This work characterizes the optimal tradeoff between the amount of common randomness used and the required rate of description.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Two familiar notions of correlation are rediscovered as extreme operating points for simulating a discrete memoryless channel, in which a channel output is generated based only on a description of the channel input.	contribution 0.56	0.71	0.14	asserted 1.00
s1	Wyner's "common information" coincides with the minimum description rate needed.	result 0.93	0.34	0.15	asserted 1.00
s2	However, when common randomness independent of the input is available, the necessary description rate reduces to Shannon's mutual information.	result 0.88	0.23	0.19	asserted 1.00
s3	This work characterizes the optimal tradeoff between the amount of common randomness used and the required rate of description.	contribution 0.96	0.91	0.72	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97.

What was examined, and what was not

sources read

arXiv listing abstract v1

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full text
figures and tables
references and citing sentences
relations to other papers

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P abstract

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S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

Two familiar notions of correlation are rediscovered as extreme operating points for simulating a discrete memoryless channel, in which a channel output is generated based only on a description of the channel input. Wyner's "common information" coincides with the minimum description rate needed. However, when common randomness independent of the input is available, the necessary description rate reduces to Shannon's mutual information. This work characterizes the optimal tradeoff between the amount of common randomness used and the required rate of description.

Human review

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How the literature uses it

2 arXiv papers cite this in 7 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

This work characterizes the optimal trade-off between the amount of common randomness used and the required rate of description.

Distributed Channel Synthesis · 0.98

Papers citing it · 5 sentences without a confident label

Builds on it 1 paper

Cuff's theorem [ref] regarding the trade-off between classical communication and common randomness for a non-feedback reverse Shannon theorem is a special case of Theorem [ref] below, essentially because a noisy classical channel is a special case of a quantum measurement and thus the simulation task is a special case.

The information-theoretic costs of simulating quantum measurements · Non-feedback measurement compression · 0.80

Compares with it 1 paper

Thus, Theorem [ref] below “sits in between” the communication tasks considered in Ref. [ref] and Ref. [ref] .

The information-theoretic costs of simulating quantum measurements · Non-feedback measurement compression · 0.94

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