496 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

### Thouless-Anderson-Palmer Approach for Lossy Compression

We study an ill-posed linear inverse problem, where a binary sequence will be
reproduced using a sparce matrix. According to the previous study, this model
can theoretically provide an optimal compression scheme for an arbitrary
distortion level, though the encoding procedure remains an NP-complete problem.
In this paper, we focus on the consistency condition for a dynamics model of
Markov-type to derive an iterative algorithm, following the steps of
Thouless-Anderson-Palmer's. Numerical results show that the algorithm can
empirically saturate the theoretical limit for the sparse construction of our
codes, which also is very close to the rate-distortion function.Comment: 10 pages, 3 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

### 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

### 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 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

### 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

### Statistical Mechanics of Broadcast Channels Using Low Density Parity Check Codes

We investigate the use of Gallager's low-density parity-check (LDPC) codes in
a broadcast channel, one of the fundamental models in network information
theory. Combining linear codes is a standard technique in practical network
communication schemes and is known to provide better performance than simple
timesharing methods when algebraic codes are used. The statistical physics
based analysis shows that the practical performance of the suggested method,
achieved by employing the belief propagation algorithm, is superior to that of
LDPC based timesharing codes while the best performance, when received
transmissions are optimally decoded, is bounded by the timesharing limit.Comment: 14 pages, 4 figure

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