543 research outputs found
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
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
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 common attacks in LDPCC-based public-key cryptosystems
We analyze the security and reliability of a recently proposed class of
public-key cryptosystems against attacks by unauthorized parties who have
acquired partial knowledge of one or more of the private key components and/or
of the plaintext. Phase diagrams are presented, showing critical partial
knowledge levels required for unauthorized decryptionComment: 14 pages, 6 figure
Random Graph Coloring - a Statistical Physics Approach
The problem of vertex coloring in random graphs is studied using methods of
statistical physics and probability. Our analytical results are compared to
those obtained by exact enumeration and Monte-Carlo simulations. We critically
discuss the merits and shortcomings of the various methods, and interpret the
results obtained. We present an exact analytical expression for the 2-coloring
problem as well as general replica symmetric approximated solutions for the
thermodynamics of the graph coloring problem with p colors and K-body edges.Comment: 17 pages, 9 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
Universal Behavior in Large-scale Aggregation of Independent Noisy Observations
Aggregation of noisy observations involves a difficult tradeoff between
observation quality, which can be increased by increasing the number of
observations, and aggregation quality which decreases if the number of
observations is too large. We clarify this behavior for a protypical system in
which arbitrarily large numbers of observations exceeding the system capacity
can be aggregated using lossy data compression. We show the existence of a
scaling relation between the collective error and the system capacity, and show
that large scale lossy aggregation can outperform lossless aggregation above a
critical level of observation noise. Further, we show that universal results
for scaling and critical value of noise which are independent of system
capacity can be obtained by considering asymptotic behavior when the system
capacity increases toward infinity.Comment: 10 pages, 3 figure
Perceptron capacity revisited: classification ability for correlated patterns
In this paper, we address the problem of how many randomly labeled patterns
can be correctly classified by a single-layer perceptron when the patterns are
correlated with each other. In order to solve this problem, two analytical
schemes are developed based on the replica method and Thouless-Anderson-Palmer
(TAP) approach by utilizing an integral formula concerning random rectangular
matrices. The validity and relevance of the developed methodologies are shown
for one known result and two example problems. A message-passing algorithm to
perform the TAP scheme is also presented
Average error exponent in Gallager low-density parity-check codes
We present a theoretical method for a direct evaluation of the average error exponent in Gallager error-correcting codes using methods of statistical physics. Results for the binary symmetric channel(BSC)are presented for codes of both finite and infinite connectivity
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