466 research outputs found
Rational Maps and Maximum Likelihood Decodings
This paper studies maximum likelihood(ML) decoding in error-correcting codes
as rational maps and proposes an approximate ML decoding rule by using a Taylor
expansion. The point for the Taylor expansion, which will be denoted by in
the paper, is properly chosen by considering some dynamical system properties.
We have two results about this approximate ML decoding. The first result proves
that the order of the first nonlinear terms in the Taylor expansion is
determined by the minimum distance of its dual code. As the second result, we
give numerical results on bit error probabilities for the approximate ML
decoding. These numerical results show better performance than that of BCH
codes, and indicate that this proposed method approximates the original ML
decoding very well.Comment: 22 pages, 4 figure
Compressive Sampling for Remote Control Systems
In remote control, efficient compression or representation of control signals
is essential to send them through rate-limited channels. For this purpose, we
propose an approach of sparse control signal representation using the
compressive sampling technique. The problem of obtaining sparse representation
is formulated by cardinality-constrained L2 optimization of the control
performance, which is reducible to L1-L2 optimization. The low rate random
sampling employed in the proposed method based on the compressive sampling, in
addition to the fact that the L1-L2 optimization can be effectively solved by a
fast iteration method, enables us to generate the sparse control signal with
reduced computational complexity, which is preferable in remote control systems
where computation delays seriously degrade the performance. We give a
theoretical result for control performance analysis based on the notion of
restricted isometry property (RIP). An example is shown to illustrate the
effectiveness of the proposed approach via numerical experiments
Capacity and Modulations with Peak Power Constraint
A practical communication channel often suffers from constraints on input
other than the average power, such as the peak power constraint. In order to
compare achievable rates with different constellations as well as the channel
capacity under such constraints, it is crucial to take these constraints into
consideration properly. In this paper, we propose a direct approach to compare
the achievable rates of practical input constellations and the capacity under
such constraints. As an example, we study the discrete-time complex-valued
additive white Gaussian noise (AWGN) channel and compare the capacity under the
peak power constraint with the achievable rates of phase shift keying (PSK) and
quadrature amplitude modulation (QAM) input constellations.Comment: 9 pages with 12 figures. Preparing for submissio
Multiuser Detection by MAP Estimation with Sum-of-Absolute-Values Relaxation
In this article, we consider multiuser detection that copes with multiple
access interference caused in star-topology machine-to-machine (M2M)
communications. We assume that the transmitted signals are discrete-valued
(e.g. binary signals taking values of ), which is taken into account as
prior information in detection. We formulate the detection problem as the
maximum a posteriori (MAP) estimation, which is relaxed to a convex
optimization called the sum-of-absolute-values (SOAV) optimization. The SOAV
optimization can be efficiently solved by a proximal splitting algorithm, for
which we give the proximity operator in a closed form. Numerical simulations
are shown to illustrate the effectiveness of the proposed approach compared
with the linear minimum mean-square-error (LMMSE) and the least absolute
shrinkage and selection operator (LASSO) methods.Comment: submitted; 6 pages, 7 figure
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