531 research outputs found
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
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
Numerical Study of TAP Metastable States in 3-body Ising Spin Glasses
The distribution of solutions of the Thouless-Anderson-Palmer equation is
studied by extensive numerical experiments for fully connected 3-body
interaction Ising spin glass models in a level of annealed calculation. A
recent study predicted that when the equilibrium state of the system is
characterized by one-step replica symmetry breaking, the distribution is
described by a Becchi-Rouet-Stora-Tyutin (BRST) supersymmetric solution in the
relatively low free energy region, whereas the BRST supersymmetry is broken for
higher values of free energy (Crisanti et al., Phys. Rev. B 71 (2005) 094202).
Our experiments qualitatively reproduce the discriminative behavior of
macroscopic variables predicted by the theoretical assessment.Comment: 13 pages, 4 figure
Statistical mechanics of typical set decoding
The performance of ``typical set (pairs) decoding'' for ensembles of
Gallager's linear code is investigated using statistical physics. In this
decoding, error happens when the information transmission is corrupted by an
untypical noise or two or more typical sequences satisfy the parity check
equation provided by the received codeword for which a typical noise is added.
We show that the average error rate for the latter case over a given code
ensemble can be tightly evaluated using the replica method, including the
sensitivity to the message length. Our approach generally improves the existing
analysis known in information theory community, which was reintroduced by
MacKay (1999) and believed as most accurate to date.Comment: 7 page
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
Analysis of CDMA systems that are characterized by eigenvalue spectrum
An approach by which to analyze the performance of the code division multiple
access (CDMA) scheme, which is a core technology used in modern wireless
communication systems, is provided. The approach characterizes the objective
system by the eigenvalue spectrum of a cross-correlation matrix composed of
signature sequences used in CDMA communication, which enables us to handle a
wider class of CDMA systems beyond the basic model reported by Tanaka. The
utility of the novel scheme is shown by analyzing a system in which the
generation of signature sequences is designed for enhancing the orthogonality.Comment: 7 pages, 2 figure
Typical Performance of Gallager-type Error-Correcting Codes
The performance of Gallager's error-correcting code is investigated via
methods of statistical physics. In this approach, the transmitted codeword
comprises products of the original message bits selected by two
randomly-constructed sparse matrices; the number of non-zero row/column
elements in these matrices constitutes a family of codes. We show that
Shannon's channel capacity is saturated for many of the codes while slightly
lower performance is obtained for others which may be of higher practical
relevance. Decoding aspects are considered by employing the TAP approach which
is identical to the commonly used belief-propagation-based decoding.Comment: 6 pages, latex, 1 figur
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
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
- …