8 research outputs found
A Generalized Cut-Set Bound for Deterministic Multi-Flow Networks and its Applications
We present a new outer bound for the sum capacity of general multi-unicast
deterministic networks. Intuitively, this bound can be understood as applying
the cut-set bound to concatenated copies of the original network with a special
restriction on the allowed transmit signal distributions. We first study
applications to finite-field networks, where we obtain a general outer-bound
expression in terms of ranks of the transfer matrices. We then show that, even
though our outer bound is for deterministic networks, a recent result relating
the capacity of AWGN KxKxK networks and the capacity of a deterministic
counterpart allows us to establish an outer bound to the DoF of KxKxK wireless
networks with general connectivity. This bound is tight in the case of the
"adjacent-cell interference" topology, and yields graph-theoretic necessary and
sufficient conditions for K DoF to be achievable in general topologies.Comment: A shorter version of this paper will appear in the Proceedings of
ISIT 201
Linear Network Coding for Two-Unicast- Networks: A Commutative Algebraic Perspective and Fundamental Limits
We consider a two-unicast- network over a directed acyclic graph of unit
capacitated edges; the two-unicast- network is a special case of two-unicast
networks where one of the destinations has apriori side information of the
unwanted (interfering) message. In this paper, we settle open questions on the
limits of network coding for two-unicast- networks by showing that the
generalized network sharing bound is not tight, vector linear codes outperform
scalar linear codes, and non-linear codes outperform linear codes in general.
We also develop a commutative algebraic approach to deriving linear network
coding achievability results, and demonstrate our approach by providing an
alternate proof to the previous results of C. Wang et. al., I. Wang et. al. and
Shenvi et. al. regarding feasibility of rate in the network.Comment: A short version of this paper is published in the Proceedings of The
IEEE International Symposium on Information Theory (ISIT), June 201
Precoding-Based Network Alignment For Three Unicast Sessions
We consider the problem of network coding across three unicast sessions over
a directed acyclic graph, where each sender and the receiver is connected to
the network via a single edge of unit capacity. We consider a network model in
which the middle of the network only performs random linear network coding, and
restrict our approaches to precoding-based linear schemes, where the senders
use precoding matrices to encode source symbols. We adapt a precoding-based
interference alignment technique, originally developed for the wireless
interference channel, to construct a precoding-based linear scheme, which we
refer to as as a {\em precoding-based network alignment scheme (PBNA)}. A
primary difference between this setting and the wireless interference channel
is that the network topology can introduce dependencies between elements of the
transfer matrix, which we refer to as coupling relations, and can potentially
affect the achievable rate of PBNA. We identify all possible such coupling
relations, and interpret these coupling relations in terms of network topology
and present polynomial-time algorithms to check the presence of these coupling
relations. Finally, we show that, depending on the coupling relations present
in the network, the optimal symmetric rate achieved by precoding-based linear
scheme can take only three possible values, all of which can be achieved by
PBNA.Comment: arXiv admin note: text overlap with arXiv:1202.340