6 research outputs found
Full Diversity Unitary Precoded Integer-Forcing
We consider a point-to-point flat-fading MIMO channel with channel state
information known both at transmitter and receiver. At the transmitter side, a
lattice coding scheme is employed at each antenna to map information symbols to
independent lattice codewords drawn from the same codebook. Each lattice
codeword is then multiplied by a unitary precoding matrix and sent
through the channel. At the receiver side, an integer-forcing (IF) linear
receiver is employed. We denote this scheme as unitary precoded integer-forcing
(UPIF). We show that UPIF can achieve full-diversity under a constraint based
on the shortest vector of a lattice generated by the precoding matrix . This constraint and a simpler version of that provide design criteria for
two types of full-diversity UPIF. Type I uses a unitary precoder that adapts at
each channel realization. Type II uses a unitary precoder, which remains fixed
for all channel realizations. We then verify our results by computer
simulations in , and MIMO using different QAM
constellations. We finally show that the proposed Type II UPIF outperform the
MIMO precoding X-codes at high data rates.Comment: 12 pages, 8 figures, to appear in IEEE-TW
Delay Reduction in Multi-Hop Device-to-Device Communication using Network Coding
This paper considers the problem of reducing the broadcast decoding delay of
wireless networks using instantly decodable network coding (IDNC) based
device-to-device (D2D) communications. In a D2D configuration, devices in the
network can help hasten the recovery of the lost packets of other devices in
their transmission range by sending network coded packets. Unlike previous
works that assumed fully connected network, this paper proposes a partially
connected configuration in which the decision should be made not only on the
packet combinations but also on the set of transmitting devices. First, the
different events occurring at each device are identified so as to derive an
expression for the probability distribution of the decoding delay. The joint
optimization problem over the set of transmitting devices and the packet
combinations of each is, then, formulated. The optimal solution of the joint
optimization problem is derived using a graph theory approach by introducing
the cooperation graph and reformulating the problem as a maximum weight clique
problem in which the weight of each vertex is the contribution of the device
identified by the vertex. Through extensive simulations, the decoding delay
experienced by all devices in the Point to Multi-Point (PMP) configuration, the
fully connected D2D (FC-D2D) configuration and the more practical partially
connected D2D (PC-D2D) configuration are compared. Numerical results suggest
that the PC-D2D outperforms the FC-D2D and provides appreciable gain especially
for poorly connected networks
-free Partition and Cover Numbers and Application
-free graphs-- also known as cographs, complement-reducible graphs, or hereditary Dacey graphs--have been well studied in graph theory.
Motivated by computer science and information theory applications, our work encodes (flat) joint probability distributions and Boolean functions as bipartite graphs and studies bipartite -free graphs.
For these applications, the graph properties of edge partitioning and covering a bipartite graph using the minimum number of these graphs are particularly relevant.
Previously, such graph properties have appeared in leakage-resilient cryptography and (variants of) coloring problems.
Interestingly, our covering problem is closely related to the well-studied problem of product/Prague dimension of loopless undirected graphs, which allows us to employ algebraic lower-bounding techniques for the product/Prague dimension.
We prove that computing these numbers is \npol-complete, even for bipartite graphs.
We establish a connection to the (unsolved) Zarankiewicz problem to show that there are bipartite graphs with size- partite sets such that these numbers are at least , for .
Finally, we accurately estimate these numbers for bipartite graphs encoding well-studied Boolean functions from circuit complexity, such as set intersection, set disjointness, and inequality.
For applications in information theory and communication \& cryptographic complexity, we consider a system where a setup samples from a (flat) joint distribution and gives the participants, Alice and Bob, their portion from this joint sample.
Alice and Bob\u27s objective is to non-interactively establish a shared key and extract the left-over entropy from their portion of the samples as independent private randomness.
A genie, who observes the joint sample, provides appropriate assistance to help Alice and Bob with their objective.
Lower bounds to the minimum size of the genie\u27s assistance translate into communication and cryptographic lower bounds.
We show that (the of) the -free partition number of a graph encoding the joint distribution that the setup uses is equivalent to the size of the genie\u27s assistance.
Consequently, the joint distributions corresponding to the bipartite graphs constructed above with high -free partition numbers correspond to joint distributions requiring more assistance from the genie.
As a representative application in non-deterministic communication complexity, we study the communication complexity of nondeterministic protocols augmented by access to the equality oracle at the output.
We show that (the of) the -free cover number of the bipartite graph encoding a Boolean function is equivalent to the minimum size of the nondeterministic input required by the parties (referred to as the communication complexity of in this model).
Consequently, the functions corresponding to the bipartite graphs with high -free cover numbers have high communication complexity.
Furthermore, there are functions with communication complexity close to the \naive protocol where the nondeterministic input reveals a party\u27s input.
Finally, the access to the equality oracle reduces the communication complexity of computing set disjointness by a constant factor in contrast to the model where parties do not have access to the equality oracle.
To compute the inequality function, we show an exponential reduction in the communication complexity, and this bound is optimal.
On the other hand, access to the equality oracle is (nearly) useless for computing set intersection