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IEEE Transactions on Information Theory

Common Randomness Generation From Finite Compound Sources Aided by One-Way Communication

Rami Ezzine, Moritz Wiese, Christian Deppe, Holger Boche

Published Aug 4, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1109/tit.2025.3595704

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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.
In the classical secret-key generation model, common randomness is generated by two terminals based on the observation of correlated components of a common source, while keeping it secret from a non-legitimate observer. It is assumed that the statistics of the source are known to all participants. In this paper, the secret-key generation based on a compound source is studied where the realization of the source statistic is unknown. The protocol should guarantee the security and reliability of the generated secret-key, simultaneously for all possible realizations of the compound source. A single-letter lower-bound of the secret-key capacity for a finite compound source is derived as a function of the public communication rate constraint. A multi-letter capacity formula is further computed for a finite compound source for the case in which the public communication is unconstrained. Finally, a single-letter capacity formula is derived for a degraded compound source with an arbitrary (possibly infinite) set of source states and a finite set of marginal states.
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.
In the classical secret-key generation model, common randomness is generated by two terminals based on the observation of correlated components of a common source, while keeping it secret from a non-legitimate observer. It is assumed that the statistics of the source are known to all participants. In this paper, the secret-key generation based on a compound source is studied where the realization of the source statistic is unknown. The protocol should guarantee the security and reliability of the generated secret-key, simultaneously for all possible realizations of the compound source. A single-letter lower-bound of the secret-key capacity for a finite compound source is derived as a function of the public communication rate constraint. A multi-letter capacity formula is further computed for a finite compound source for the case in which the public communication is unconstrained. Finally, a single-letter capacity formula is derived for a degraded compound source with an arbitrary (possibly infinite) set of source states and a finite set of marginal states.
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 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.