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Summary: IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 44, NO. 1, JANUARY 1998 215
The Common Randomness Capacity of a Pair of
Independent Discrete Memoryless Channels
Sivarama Venkatesan, Student Member, IEEE, and Venkat Anantharam, Member, IEEE
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 HA and HB,
respectively, we show that they can generate common randomness
at a rate of maxfmin[HA + H(W j Q); I(P ; V )] + min[HB +
H(V j P ); I(Q; W )]g 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.
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