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IEEE International Symposium on Information Theory (ISIT)

Common Randomness Generation from Sources with Infinite Polish Alphabets

Wafa Labidi, Rami Ezzine, Moritz Wiese, Christian Deppe, Holger Boche

Published Jun 22, 2025• 1 citation
Publisher

Abstract

We study the problem of common randomness (CR) generation in a fundamental two-party communication scenario, where a sender and a receiver seek to agree-with high probability-on a shared random variable. Both parties observe independent and identically distributed (i.i.d.) samples from sources defined over a Polish alphabet with an arbitrary joint distribution. Communication is restricted to a unidirectional, minimally interactive exchange over a noisy, memoryless channel. For this setting, we establish single-letter lower and upper bounds on the CR capacity. These bounds coincide except possibly at a countable set of points where discontinuities may arise.

DOI
10.1109/isit63088.2025.11195591

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We study the problem of common randomness (CR) generation in a fundamental two-party communication scenario, where a sender and a receiver seek to agree-with high probability-on a shared random variable. Both parties observe independent and identically distributed (i.i.d.) samples from sources defined over a Polish alphabet with an arbitrary joint distribution. Communication is restricted to a unidirectional, minimally interactive exchange over a noisy, memoryless channel. For this setting, we establish single-letter lower and upper bounds on the CR capacity. These bounds coincide except possibly at a countable set of points where discontinuities may arise.
We investigate the problem of common randomness (CR) generation in the basic two-party communication setting in which a sender and a receiver aim to agree on a common random variable with high probability. The terminals observe independent and identically distributed (i.i.d.) samples of sources with an arbitrary distribution defined on a Polish alphabet and are allowed to communicate as little as possible over a noisy, memoryless channel. We establish single-letter upper and lower bounds on the CR capacity for the specified model. The derived bounds hold with equality except for at most countably many points where discontinuity issues might arise.
We study a two-source model for common randomness (CR) generation in which the sender Alice and the receiver Bob generate a common random variable with a high probability of agreement by observing independent and identically distributed (i.i.d.) samples of correlated sources on countably infinite alphabets. The two parties are additionally allowed to communicate over a noisy memoryless channel. In our work, we establish a single-letter lower and upper-bound on the CR capacity for the proposed model. This is a challenging scenario because some of the finite alphabet properties, namely of the entropy can not be extended to the countably infinite case. We use a generalized typicality criterion, called unified typicality, which can be applied to random variables on countably infinite alphabets.
We study the problem of common randomness (CR) generation in the basic two-party communication setting in which the sender and the receiver aim to agree on a common random variable with high probability by observing independent and identically distributed (i.i.d.) samples of correlated Gaussian sources and while communicating as little as possible over a noisy memoryless channel. We completely solve the problem by giving a single-letter characterization of the CR capacity for the proposed model and by providing rigorous proof of it We prove that the CR capacity is infinite when the Gaussian sources are perfectly correlated.
We investigate the problem of generating common randomness (CR) from finite compound sources aided by unidirectional communication over rate-limited perfect channels. The two communicating parties, often referred to as terminals, observe independent and identically distributed (i.i.d.) samples of a finite compound source and aim to agree on a common random variable with a high probability for every possible realization of the source state. Both parties know the set of source states as well as their statistics. However, they are unaware of the actual realization of the source state. We establish a single-letter lower and upper bound on the compound CR capacity for the specified model. Furthermore, we present two special scenarios where the established bounds coincide.
We investigate the problem of generating common randomness (CR) from a finite compound source aided by unidirectional communication over a rate-limited perfect channel. The two communicating parties observe independent and identically distributed (i.i.d.) samples of a finite compound source and aim to agree on a common random variable with high probability for every possible state. Both parties know the set of source states as well as their statistics. However, they don’t know the actual state. We establish a single-letter formula for the compound CR capacity in the presence of communication over the channel and study key properties of the compound CR capacity: superadditivity, concavity, and continuity. We also consider the case where there is no communication between the terminals, and only the source outputs observed by the terminal at the receiving end of the perfect channel are state-dependent. In this setting, we establish single-letter bounds on the compound CR capacity. The single-letter lower bound is derived under the assumption that the source distributions are pairwise distinct for all states. Finally, within the same setting, we propose a CR generation scheme for a two-state binary source example. Notably, this scheme does not depend on the previously mentioned assumption.
We consider a standard two-source model for uniform common randomness (UCR) generation, in which Alice and Bob observe independent and identically distributed (i. i. d.) samples of a correlated finite source and where Alice is allowed to send information to Bob over an arbitrary single-user channel. We study the ϵ-UCR capacity for the proposed model, defined as the maximum common randomness rate one can achieve such that the probability that Alice and Bob do not agree on a common uniform or nearly uniform random variable does not exceed ϵ. We establish a lower and an upper bound on the ϵ-UCR capacity using the bounds on the ϵ-transmission capacity proved by Verdú and Han for arbitrary point-to-point channels.A detailed version with all proofs, explanations and more discussions can be found in [1].