119 research outputs found
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
Computation Over Gaussian Networks With Orthogonal Components
Function computation of arbitrarily correlated discrete sources over Gaussian
networks with orthogonal components is studied. Two classes of functions are
considered: the arithmetic sum function and the type function. The arithmetic
sum function in this paper is defined as a set of multiple weighted arithmetic
sums, which includes averaging of the sources and estimating each of the
sources as special cases. The type or frequency histogram function counts the
number of occurrences of each argument, which yields many important statistics
such as mean, variance, maximum, minimum, median, and so on. The proposed
computation coding first abstracts Gaussian networks into the corresponding
modulo sum multiple-access channels via nested lattice codes and linear network
coding and then computes the desired function by using linear Slepian-Wolf
source coding. For orthogonal Gaussian networks (with no broadcast and
multiple-access components), the computation capacity is characterized for a
class of networks. For Gaussian networks with multiple-access components (but
no broadcast), an approximate computation capacity is characterized for a class
of networks.Comment: 30 pages, 12 figures, submitted to IEEE Transactions on Information
Theor
Interference alignment for the MIMO interference channel
We study vector space interference alignment for the MIMO interference
channel with no time or frequency diversity, and no symbol extensions. We prove
both necessary and sufficient conditions for alignment. In particular, we
characterize the feasibility of alignment for the symmetric three-user channel
where all users transmit along d dimensions, all transmitters have M antennas
and all receivers have N antennas, as well as feasibility of alignment for the
fully symmetric (M=N) channel with an arbitrary number of users.
An implication of our results is that the total degrees of freedom available
in a K-user interference channel, using only spatial diversity from the
multiple antennas, is at most 2. This is in sharp contrast to the K/2 degrees
of freedom shown to be possible by Cadambe and Jafar with arbitrarily large
time or frequency diversity.
Moving beyond the question of feasibility, we additionally discuss
computation of the number of solutions using Schubert calculus in cases where
there are a finite number of solutions.Comment: 16 pages, 7 figures, final submitted versio
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