172,940 research outputs found
MU-MIMO Communications with MIMO Radar: From Co-existence to Joint Transmission
Beamforming techniques are proposed for a joint multi-input-multi-output
(MIMO) radar-communication (RadCom) system, where a single device acts both as
a radar and a communication base station (BS) by simultaneously communicating
with downlink users and detecting radar targets. Two operational options are
considered, where we first split the antennas into two groups, one for radar
and the other for communication. Under this deployment, the radar signal is
designed to fall into the null-space of the downlink channel. The communication
beamformer is optimized such that the beampattern obtained matches the radar's
beampattern while satisfying the communication performance requirements. To
reduce the optimizations' constraints, we consider a second operational option,
where all the antennas transmit a joint waveform that is shared by both radar
and communications. In this case, we formulate an appropriate probing
beampattern, while guaranteeing the performance of the downlink communications.
By incorporating the SINR constraints into objective functions as penalty
terms, we further simplify the original beamforming designs to weighted
optimizations, and solve them by efficient manifold algorithms. Numerical
results show that the shared deployment outperforms the separated case
significantly, and the proposed weighted optimizations achieve a similar
performance to the original optimizations, despite their significantly lower
computational complexity.Comment: 15 pages, 15 figures. This work has been submitted to the IEEE for
possible publication. Copyright may be transferred without notice, after
which this version may no longer be accessibl
Communication Over MIMO Broadcast Channels Using Lattice-Basis Reduction
A simple scheme for communication over MIMO broadcast channels is introduced
which adopts the lattice reduction technique to improve the naive channel
inversion method. Lattice basis reduction helps us to reduce the average
transmitted energy by modifying the region which includes the constellation
points. Simulation results show that the proposed scheme performs well, and as
compared to the more complex methods (such as the perturbation method) has a
negligible loss. Moreover, the proposed method is extended to the case of
different rates for different users. The asymptotic behavior of the symbol
error rate of the proposed method and the perturbation technique, and also the
outage probability for the case of fixed-rate users is analyzed. It is shown
that the proposed method, based on LLL lattice reduction, achieves the optimum
asymptotic slope of symbol-error-rate (called the precoding diversity). Also,
the outage probability for the case of fixed sum-rate is analyzed.Comment: Submitted to IEEE Trans. on Info. Theory (Jan. 15, 2006), Revised
(Jun. 12, 2007
Low-Complexity LP Decoding of Nonbinary Linear Codes
Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has
attracted much attention in the research community in the past few years. LP
decoding has been derived for binary and nonbinary linear codes. However, the
most important problem with LP decoding for both binary and nonbinary linear
codes is that the complexity of standard LP solvers such as the simplex
algorithm remains prohibitively large for codes of moderate to large block
length. To address this problem, two low-complexity LP (LCLP) decoding
algorithms for binary linear codes have been proposed by Vontobel and Koetter,
henceforth called the basic LCLP decoding algorithm and the subgradient LCLP
decoding algorithm.
In this paper, we generalize these LCLP decoding algorithms to nonbinary
linear codes. The computational complexity per iteration of the proposed
nonbinary LCLP decoding algorithms scales linearly with the block length of the
code. A modified BCJR algorithm for efficient check-node calculations in the
nonbinary basic LCLP decoding algorithm is also proposed, which has complexity
linear in the check node degree.
Several simulation results are presented for nonbinary LDPC codes defined
over Z_4, GF(4), and GF(8) using quaternary phase-shift keying and
8-phase-shift keying, respectively, over the AWGN channel. It is shown that for
some group-structured LDPC codes, the error-correcting performance of the
nonbinary LCLP decoding algorithms is similar to or better than that of the
min-sum decoding algorithm.Comment: To appear in IEEE Transactions on Communications, 201
Interior Point Decoding for Linear Vector Channels
In this paper, a novel decoding algorithm for low-density parity-check (LDPC)
codes based on convex optimization is presented. The decoding algorithm, called
interior point decoding, is designed for linear vector channels. The linear
vector channels include many practically important channels such as inter
symbol interference channels and partial response channels. It is shown that
the maximum likelihood decoding (MLD) rule for a linear vector channel can be
relaxed to a convex optimization problem, which is called a relaxed MLD
problem. The proposed decoding algorithm is based on a numerical optimization
technique so called interior point method with barrier function. Approximate
variations of the gradient descent and the Newton methods are used to solve the
convex optimization problem. In a decoding process of the proposed algorithm, a
search point always lies in the fundamental polytope defined based on a
low-density parity-check matrix. Compared with a convectional joint message
passing decoder, the proposed decoding algorithm achieves better BER
performance with less complexity in the case of partial response channels in
many cases.Comment: 18 pages, 17 figures, The paper has been submitted to IEEE
Transaction on Information Theor
Fast Min-Sum Algorithms for Decoding of LDPC over GF(q)
In this paper, we present a fast min-sum algorithm for decoding LDPC codes
over GF(q). Our algorithm is different from the one presented by David Declercq
and Marc Fossorier in ISIT 05 only at the way of speeding up the horizontal
scan in the min-sum algorithm. The Declercq and Fossorier's algorithm speeds up
the computation by reducing the number of configurations, while our algorithm
uses the dynamic programming instead. Compared with the configuration reduction
algorithm, the dynamic programming one is simpler at the design stage because
it has less parameters to tune. Furthermore, it does not have the performance
degradation problem caused by the configuration reduction because it searches
the whole configuration space efficiently through dynamic programming. Both
algorithms have the same level of complexity and use simple operations which
are suitable for hardware implementations.Comment: Accepted by IEEE Information Theory Workshop, Chengdu, China, 200
Asymptotic tensor rank of graph tensors: beyond matrix multiplication
We present an upper bound on the exponent of the asymptotic behaviour of the
tensor rank of a family of tensors defined by the complete graph on
vertices. For , we show that the exponent per edge is at most 0.77,
outperforming the best known upper bound on the exponent per edge for matrix
multiplication (), which is approximately 0.79. We raise the question
whether for some the exponent per edge can be below , i.e. can
outperform matrix multiplication even if the matrix multiplication exponent
equals 2. In order to obtain our results, we generalise to higher order tensors
a result by Strassen on the asymptotic subrank of tight tensors and a result by
Coppersmith and Winograd on the asymptotic rank of matrix multiplication. Our
results have applications in entanglement theory and communication complexity
Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithms
Mathematical programming is a branch of applied mathematics and has recently
been used to derive new decoding approaches, challenging established but often
heuristic algorithms based on iterative message passing. Concepts from
mathematical programming used in the context of decoding include linear,
integer, and nonlinear programming, network flows, notions of duality as well
as matroid and polyhedral theory. This survey article reviews and categorizes
decoding methods based on mathematical programming approaches for binary linear
codes over binary-input memoryless symmetric channels.Comment: 17 pages, submitted to the IEEE Transactions on Information Theory.
Published July 201
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