ISSN 0032-9460, Problems of Information Transmission, 2014, Vol. 50, No. 1, pp. 15–26.
Pleiades Publishing, Inc., 2014.
Original Russian Text
M. Wiese, H. Boche, 2014, published in Problemy Peredachi Informatsii, 2014, Vol. 50, No. 1, pp. 18–30.
On the Weakest Resource for Coordination
in Arbitrarily Varying Multiple Access Channels
with Conferencing Encoders
M. Wiese and H. Boche
Technische Universit¨at M¨unchen, Germany
Received June 14, 2013
Abstract—If senders and a receiver of an arbitrarily varying multiple-access channel (AV-
MAC) have access to outputs of discrete correlated memoryless sources, the same rate region
is achievable as if common randomness were available, no matter how small the correlation is.
This reduces the necessary amount of cooperation in an AV-MAC considerably. Moreover, to
transmit blocklength-n words, no more than order log n source outputs are required.
Arbitrarily varying channels (AVCs) and arbitrarily varying multiple access channels (AV-
MACs) are examples of channels where deterministic coding must not be confused with randomness
assisted coding. Ahlswede observed that in AVCs there is a dichotomy: the deterministic capacity
of an AVC, i.e., the capacity achievable with deterministic coding, either equals the randomness
assisted capacity, i.e., the capacity where the code is chosen according to a random parameter
known to all communicating parties, or equals zero . Csisz´ar and Narayan showed that the dis-
criminating property is symmetrizability as introduced by Ericson : the deterministic capacity
of an AVC equals zero if and only if the channel is symmetrizable .
If senders of an AV-MAC are allowed to do Willems conferencing at positive rates C
situation is similar. Willems conferencing was introduced by Willems in [4, 5]. This iterative way
of encoder cooperation interpolates between the traditional noncooperative case (C
and the case where the two senders can be treated as one (C
= ∞). The symmetrizability
condition applied in this case is Ericson’s if the senders of the AV-MAC are considered to be one.
One obtains a dichotomy similar to the AVC case: symmetrizability means that no message can be
transmitted deterministically, otherwise deterministic coding achieves the same capacity region as
randomness assisted coding . The two other symmetrizability conditions for AV-MACs as deﬁned
by Gubner  do not play a role in the AV-MAC with conferencing encoders. These two conditions
are called X -symmetrizability and Y-symmetrizability, whereas the type of symmetrizability that
we use is called XY-symmetrizability in the AV-MAC context.
Randomness assisted coding means that both the sender(s) and the receiver know the outcome
of a single random experiment which then is used to select the codewords and decoding set for a
given message (pair). The only restriction on the random experiment is that the number of possible
outcomes is ﬁnite.
Supported in part by the German National Science Foundation (DFG), project nos. BO 1734/23-1 and
BO 1734/24-1, in the COIN Focus Program.