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IEEE Transactions on Information Theory

The common randomness capacity of a pair of independent discrete memoryless channels

Sivarama Venkatesan, Venkat Anantharam

Published Jan 1, 1998• 35 citations
Publisher

Abstract

We study the following problem: two agents Alice and Bob are connected to each other by independent discrete memoryless channels. They wish to generate common randomness, i.e. agree on a common random variable, by communicating interactively over the two channels. Assuming that Alice and Bob are allowed access to independent external random sources at rates (in bits per step of communication) of H/sub A/ and H/sub B/, respectively, we show that they can generate common randomness at a rate of max{min[H/sub A/+H(W|Q),I(P;V)]+min[H/sub B/+H(V|P), I(Q;W)]} bits per step, by exploiting the noise on the two channels. Here, V is the channel from Alice to Bob, and W is the channel from Bob to Alice. The maximum is over all probability distributions P and Q on the input alphabets of V and W, respectively. We also prove a strong converse which establishes the above rate as the highest attainable in this situation.

DOI
10.1109/18.651022

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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 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.
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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.