586 research outputs found
A Mean-field Approach for an Intercarrier Interference Canceller for OFDM
The similarity of the mathematical description of random-field spin systems
to orthogonal frequency-division multiplexing (OFDM) scheme for wireless
communication is exploited in an intercarrier-interference (ICI) canceller used
in the demodulation of OFDM. The translational symmetry in the Fourier domain
generically concentrates the major contribution of ICI from each subcarrier in
the subcarrier's neighborhood. This observation in conjunction with mean field
approach leads to a development of an ICI canceller whose necessary cost of
computation scales linearly with respect to the number of subcarriers. It is
also shown that the dynamics of the mean-field canceller are well captured by a
discrete map of a single macroscopic variable, without taking the spatial and
time correlations of estimated variables into account.Comment: 7pages, 3figure
Critical Noise Levels for LDPC decoding
We determine the critical noise level for decoding low density parity check
error correcting codes based on the magnetization enumerator (\cM), rather
than on the weight enumerator (\cW) employed in the information theory
literature. The interpretation of our method is appealingly simple, and the
relation between the different decoding schemes such as typical pairs decoding,
MAP, and finite temperature decoding (MPM) becomes clear. In addition, our
analysis provides an explanation for the difference in performance between MN
and Gallager codes. Our results are more optimistic than those derived via the
methods of information theory and are in excellent agreement with recent
results from another statistical physics approach.Comment: 9 pages, 5 figure
Statistical Mechanics of Dictionary Learning
Finding a basis matrix (dictionary) by which objective signals are
represented sparsely is of major relevance in various scientific and
technological fields. We consider a problem to learn a dictionary from a set of
training signals. We employ techniques of statistical mechanics of disordered
systems to evaluate the size of the training set necessary to typically succeed
in the dictionary learning. The results indicate that the necessary size is
much smaller than previously estimated, which theoretically supports and/or
encourages the use of dictionary learning in practical situations.Comment: 6 pages, 4 figure
Error-correcting code on a cactus: a solvable model
An exact solution to a family of parity check error-correcting codes is
provided by mapping the problem onto a Husimi cactus. The solution obtained in
the thermodynamic limit recovers the replica symmetric theory results and
provides a very good approximation to finite systems of moderate size. The
probability propagation decoding algorithm emerges naturally from the analysis.
A phase transition between decoding success and failure phases is found to
coincide with an information-theoretic upper bound. The method is employed to
compare Gallager and MN codes.Comment: 7 pages, 3 figures, with minor correction
Survey propagation for the cascading Sourlas code
We investigate how insights from statistical physics, namely survey
propagation, can improve decoding of a particular class of sparse error
correcting codes. We show that a recently proposed algorithm, time averaged
belief propagation, is in fact intimately linked to a specific survey
propagation for which Parisi's replica symmetry breaking parameter is set to
zero, and that the latter is always superior to belief propagation in the high
connectivity limit. We briefly look at further improvements available by going
to the second level of replica symmetry breaking.Comment: 14 pages, 5 figure
Parallel dynamics of continuous Hopfield model revisited
We have applied the generating functional analysis (GFA) to the continuous
Hopfield model. We have also confirmed that the GFA predictions in some typical
cases exhibit good consistency with computer simulation results. When a
retarded self-interaction term is omitted, the GFA result becomes identical to
that obtained using the statistical neurodynamics as well as the case of the
sequential binary Hopfield model.Comment: 4 pages, 2 figure
Magnetization enumerator of real-valued symmetric channels in Gallager error-correcting codes
Using the magnetization enumerator method, we evaluate the practical and
theoretical limitations of symmetric channels with real outputs. Results are
presented for several regular Gallager code constructions.Comment: 5 pages, 1 figure, to appear as Brief Report in Physical Review
On-line learning of non-monotonic rules by simple perceptron
We study the generalization ability of a simple perceptron which learns
unlearnable rules. The rules are presented by a teacher perceptron with a
non-monotonic transfer function. The student is trained in the on-line mode.
The asymptotic behaviour of the generalization error is estimated under various
conditions. Several learning strategies are proposed and improved to obtain the
theoretical lower bound of the generalization error.Comment: LaTeX 20 pages using IOP LaTeX preprint style file, 14 figure
Generating functional analysis of CDMA detection dynamics
We investigate the detection dynamics of the parallel interference canceller
(PIC) for code-division multiple-access (CDMA) multiuser detection, applied to
a randomly spread, fully syncronous base-band uncoded CDMA channel model with
additive white Gaussian noise (AWGN) under perfect power control in the
large-system limit. It is known that the predictions of the density evolution
(DE) can fairly explain the detection dynamics only in the case where the
detection dynamics converge. At transients, though, the predictions of DE
systematically deviate from computer simulation results. Furthermore, when the
detection dynamics fail to convergence, the deviation of the predictions of DE
from the results of numerical experiments becomes large. As an alternative,
generating functional analysis (GFA) can take into account the effect of the
Onsager reaction term exactly and does not need the Gaussian assumption of the
local field. We present GFA to evaluate the detection dynamics of PIC for CDMA
multiuser detection. The predictions of GFA exhibits good consistency with the
computer simulation result for any condition, even if the dynamics fail to
convergence.Comment: 14 pages, 3 figure
Statistical mechanical analysis of the linear vector channel in digital communication
A statistical mechanical framework to analyze linear vector channel models in
digital wireless communication is proposed for a large system. The framework is
a generalization of that proposed for code-division multiple-access systems in
Europhys. Lett. 76 (2006) 1193 and enables the analysis of the system in which
the elements of the channel transfer matrix are statistically correlated with
each other. The significance of the proposed scheme is demonstrated by
assessing the performance of an existing model of multi-input multi-output
communication systems.Comment: 15 pages, 2 figure
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