The common randomness capacity of a pair of independent discretememoryless channels
Venkatesan, S.
Anantharam, V.
Cornell Univ., Ithaca, NY;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: Jan 1998
Volume: 44,
Issue: 1
On page(s): 215-224
ISSN: 0018-9448
References Cited: 12
CODEN: IETTAW
INSPEC Accession Number: 5812015
Digital Object Identifier: 10.1109/18.651022
Current Version Published: 2002-08-06
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 max{min[HA+H(W|Q),I(P;V)]+min[HB
+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
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