383 research outputs found
Finite-Connectivity Spin-Glass Phase Diagrams and Low Density Parity Check Codes
We obtain phase diagrams of regular and irregular finite connectivity
spin-glasses. Contact is firstly established between properties of the phase
diagram and the performances of low density parity check codes (LDPC) within
the Replica Symmetric (RS) ansatz. We then study the location of the dynamical
and critical transition of these systems within the one step Replica Symmetry
Breaking theory (RSB), extending similar calculations that have been performed
in the past for the Bethe spin-glass problem. We observe that, away from the
Nishimori line, in the low temperature region, the location of the dynamical
transition line does change within the RSB theory, in comparison with the (RS)
case. For LDPC decoding over the binary erasure channel we find, at zero
temperature and rate R=1/4 an RS critical transition point located at p_c =
0.67 while the critical RSB transition point is located at p_c = 0.7450, to be
compared with the corresponding Shannon bound 1-R. For the binary symmetric
channel (BSC) we show that the low temperature reentrant behavior of the
dynamical transition line, observed within the RS ansatz, changes within the
RSB theory; the location of the dynamical transition point occurring at higher
values of the channel noise. Possible practical implications to improve the
performances of the state-of-the-art error correcting codes are discussed.Comment: 21 pages, 15 figure
Finite size effects and error-free communication in Gaussian channels
The efficacy of a specially constructed Gallager-type error-correcting code
to communication in a Gaussian channel is being examined. The construction is
based on the introduction of complex matrices, used in both encoding and
decoding, which comprise sub-matrices of cascading connection values. The
finite size effects are estimated for comparing the results to the bounds set
by Shannon. The critical noise level achieved for certain code-rates and
infinitely large systems nearly saturates the bounds set by Shannon even when
the connectivity used is low
Cryptographical Properties of Ising Spin Systems
The relation between Ising spin systems and public-key cryptography is
investigated using methods of statistical physics. The insight gained from the
analysis is used for devising a matrix-based cryptosystem whereby the
ciphertext comprises products of the original message bits; these are selected
by employing two predetermined randomly-constructed sparse matrices. The
ciphertext is decrypted using methods of belief-propagation. The analyzed
properties of the suggested cryptosystem show robustness against various
attacks and competitive performance to modern cyptographical methods.Comment: 4 pages, 2 figure
Assessing and countering reaction attacks against post-quantum public-key cryptosystems based on QC-LDPC codes
Code-based public-key cryptosystems based on QC-LDPC and QC-MDPC codes are
promising post-quantum candidates to replace quantum vulnerable classical
alternatives. However, a new type of attacks based on Bob's reactions have
recently been introduced and appear to significantly reduce the length of the
life of any keypair used in these systems. In this paper we estimate the
complexity of all known reaction attacks against QC-LDPC and QC-MDPC code-based
variants of the McEliece cryptosystem. We also show how the structure of the
secret key and, in particular, the secret code rate affect the complexity of
these attacks. It follows from our results that QC-LDPC code-based systems can
indeed withstand reaction attacks, on condition that some specific decoding
algorithms are used and the secret code has a sufficiently high rate.Comment: 21 pages, 2 figures, to be presented at CANS 201
Statistical mechanics of lossy compression for non-monotonic multilayer perceptrons
A lossy data compression scheme for uniformly biased Boolean messages is
investigated via statistical mechanics techniques. We utilize tree-like
committee machine (committee tree) and tree-like parity machine (parity tree)
whose transfer functions are non-monotonic. The scheme performance at the
infinite code length limit is analyzed using the replica method. Both committee
and parity treelike networks are shown to saturate the Shannon bound. The AT
stability of the Replica Symmetric solution is analyzed, and the tuning of the
non-monotonic transfer function is also discussed.Comment: 29 pages, 7 figure
Statistical mechanics of error exponents for error-correcting codes
Error exponents characterize the exponential decay, when increasing message
length, of the probability of error of many error-correcting codes. To tackle
the long standing problem of computing them exactly, we introduce a general,
thermodynamic, formalism that we illustrate with maximum-likelihood decoding of
low-density parity-check (LDPC) codes on the binary erasure channel (BEC) and
the binary symmetric channel (BSC). In this formalism, we apply the cavity
method for large deviations to derive expressions for both the average and
typical error exponents, which differ by the procedure used to select the codes
from specified ensembles. When decreasing the noise intensity, we find that two
phase transitions take place, at two different levels: a glass to ferromagnetic
transition in the space of codewords, and a paramagnetic to glass transition in
the space of codes.Comment: 32 pages, 13 figure
Opportunistic linked data querying through approximate membership metadata
Between URI dereferencing and the SPARQL protocol lies a largely unexplored axis of possible interfaces to Linked Data, each with its own combination of trade-offs. One of these interfaces is Triple Pattern Fragments, which allows clients to execute SPARQL queries against low-cost servers, at the cost of higher bandwidth. Increasing a client's efficiency means lowering the number of requests, which can among others be achieved through additional metadata in responses. We noted that typical SPARQL query evaluations against Triple Pattern Fragments require a significant portion of membership subqueries, which check the presence of a specific triple, rather than a variable pattern. This paper studies the impact of providing approximate membership functions, i.e., Bloom filters and Golomb-coded sets, as extra metadata. In addition to reducing HTTP requests, such functions allow to achieve full result recall earlier when temporarily allowing lower precision. Half of the tested queries from a WatDiv benchmark test set could be executed with up to a third fewer HTTP requests with only marginally higher server cost. Query times, however, did not improve, likely due to slower metadata generation and transfer. This indicates that approximate membership functions can partly improve the client-side query process with minimal impact on the server and its interface
Secure and linear cryptosystems using error-correcting codes
A public-key cryptosystem, digital signature and authentication procedures
based on a Gallager-type parity-check error-correcting code are presented. The
complexity of the encryption and the decryption processes scale linearly with
the size of the plaintext Alice sends to Bob. The public-key is pre-corrupted
by Bob, whereas a private-noise added by Alice to a given fraction of the
ciphertext of each encrypted plaintext serves to increase the secure channel
and is the cornerstone for digital signatures and authentication. Various
scenarios are discussed including the possible actions of the opponent Oscar as
an eavesdropper or as a disruptor
Analysis of reaction and timing attacks against cryptosystems based on sparse parity-check codes
In this paper we study reaction and timing attacks against cryptosystems
based on sparse parity-check codes, which encompass low-density parity-check
(LDPC) codes and moderate-density parity-check (MDPC) codes. We show that the
feasibility of these attacks is not strictly associated to the quasi-cyclic
(QC) structure of the code but is related to the intrinsically probabilistic
decoding of any sparse parity-check code. So, these attacks not only work
against QC codes, but can be generalized to broader classes of codes. We
provide a novel algorithm that, in the case of a QC code, allows recovering a
larger amount of information than that retrievable through existing attacks and
we use this algorithm to characterize new side-channel information leakages. We
devise a theoretical model for the decoder that describes and justifies our
results. Numerical simulations are provided that confirm the effectiveness of
our approach
Shannon Meets Carnot: Generalized Second Thermodynamic Law
The classical thermodynamic laws fail to capture the behavior of systems with
energy Hamiltonian which is an explicit function of the temperature. Such
Hamiltonian arises, for example, in modeling information processing systems,
like communication channels, as thermal systems. Here we generalize the second
thermodynamic law to encompass systems with temperature-dependent energy
levels, , where denotes averaging over
the Boltzmann distribution and reveal a new definition to the basic notion of
temperature. This generalization enables to express, for instance, the mutual
information of the Gaussian channel as a consequence of the fundamental laws of
nature - the laws of thermodynamics
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