TY - GEN

T1 - Network equivalence for a joint compound-arbitrarily-varying network model

AU - Kosut, Oliver

AU - Kliewer, Jorg

N1 - Funding Information:
This material is based upon work supported by the National Science Foundation under grants CCF-1422358 and CNS-1526547.

PY - 2016/10/21

Y1 - 2016/10/21

N2 - We consider the problem of finding the capacity of noisy networks under the presence of Byzantine adversaries, modeled by a joint compound channel and arbitrarily varying channel (AVC) model. This extends our earlier work which considers these models only in isolation. The motivation for this setup is that typically the adversary first selects an arbitrary subset of edges from the network and then specifies adversarial transmissions to each of the selected edges. We show that in some cases equivalence between this network and another network holds in the sense that for a fixed selection of adversarial edges the noisy links can be replaced by noiseless bit-pipes with a capacity equal to the random coding capacity of the corresponding AVC. In particular, the capacity region for the noisy network can be outer bounded by the intersection of the individual capacity regions for the noiseless case, for each adversarial edge selection. Moreover, if the network is fully connected, we also show that this upper bound is equivalent to the capacity of the noisy network. We also provide necessary and sufficient condition for full connectivity, making use of a new condition for an AVC termed overwritability.

AB - We consider the problem of finding the capacity of noisy networks under the presence of Byzantine adversaries, modeled by a joint compound channel and arbitrarily varying channel (AVC) model. This extends our earlier work which considers these models only in isolation. The motivation for this setup is that typically the adversary first selects an arbitrary subset of edges from the network and then specifies adversarial transmissions to each of the selected edges. We show that in some cases equivalence between this network and another network holds in the sense that for a fixed selection of adversarial edges the noisy links can be replaced by noiseless bit-pipes with a capacity equal to the random coding capacity of the corresponding AVC. In particular, the capacity region for the noisy network can be outer bounded by the intersection of the individual capacity regions for the noiseless case, for each adversarial edge selection. Moreover, if the network is fully connected, we also show that this upper bound is equivalent to the capacity of the noisy network. We also provide necessary and sufficient condition for full connectivity, making use of a new condition for an AVC termed overwritability.

UR - http://www.scopus.com/inward/record.url?scp=84998893253&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84998893253&partnerID=8YFLogxK

U2 - 10.1109/ITW.2016.7606812

DO - 10.1109/ITW.2016.7606812

M3 - Conference contribution

AN - SCOPUS:84998893253

T3 - 2016 IEEE Information Theory Workshop, ITW 2016

SP - 141

EP - 145

BT - 2016 IEEE Information Theory Workshop, ITW 2016

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2016 IEEE Information Theory Workshop, ITW 2016

Y2 - 11 September 2016 through 14 September 2016

ER -