Statistical physics of irregular low-density parity-check codes

Low-density parity-check codes with irregular constructions have recently been shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes. We use the replica method to find a phase transition which coincides with Shannon's coding bound when appropriate parameters are chosen. The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulation results. We compare the performance of irregular codes with that of regular codes and discuss the factors that contribute to the improvement in performance.

Statistical mechanics of low-density parity check error-correcting codes over Galois fields

A variation of low-density parity check (LDPC) error-correcting codes defined over Galois fields (GF(q)) is investigated using statistical physics. A code of this type is characterised by a sparse random parity check matrix composed of C non-zero elements per column. We examine the dependence of the code performance on the value of q, for finite and infinite C values, both in terms of the thermodynamical transition point and the practical decoding phase characterised by the existence of a unique (ferromagnetic) solution. We find different q-dependence in the cases of C = 2 and C ≥ 3; the analytical solutions are in agreement with simulation results, providing a quantitative measure to the improvement in performance obtained using non-binary alphabets.

Statistical physics of low density parity check error correcting codes

We study the performance of Low Density Parity Check (LDPC) error-correcting codes using the methods of statistical physics. LDPC codes are based on the generation of codewords using Boolean sums of the original message bits by employing two randomly-constructed sparse matrices. These codes can be mapped onto Ising spin models and studied using common methods of statistical physics. We examine various regular constructions and obtain insight into their theoretical and practical limitations. We also briefly report on results obtained for irregular code constructions, for codes with non-binary alphabet, and on how a finite system size effects the error probability.

Typical performance of low-density parity-check codes over general symmetric channels

Typical performance of low-density parity-check (LDPC) codes over a general binary-input output-symmetric memoryless channel is investigated using methods of statistical mechanics. The binary-input additive-white-Gaussian-noise channel and the binary-input Laplace channel are considered as specific channel noise models.

Statistical mechanics of low-density parity-check codes

We review recent theoretical progress on the statistical mechanics of error correcting codes, focusing on low-density parity-check (LDPC) codes in general, and on Gallager and MacKay-Neal codes in particular. By exploiting the relation between LDPC codes and Ising spin systems with multispin interactions, one can carry out a statistical mechanics based analysis that determines the practical and theoretical limitations of various code constructions, corresponding to dynamical and thermodynamical transitions, respectively, as well as the behaviour of error-exponents averaged over the corresponding code ensemble as a function of channel noise. We also contrast the results obtained using methods of statistical mechanics with those derived in the information theory literature, and show how these methods can be generalized to include other channel types and related communication problems.

Analysis of common attacks in public-key cryptosystems based on low-density parity-check codes

The security and reliability of a class of public-key cryptosystems against attacks by unauthorized parties, who had acquired partial knowledge of one or more of the private key components and/or of the message, were discussed. The standard statistical mechanical methods of dealing with diluted spin systems with replica symmetric considerations were analyzed. The dynamical transition which defined decryption success in practical situation was studied. The phase diagrams which showed the dynamical threshold as a function of the partial acquired knowledge of the private key were also presented.

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 degraded 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 time sharing 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 time sharing codes while the best performance, when received transmissions are optimally decoded, is bounded by the time sharing limit.

Global and physical self-esteem and body dissatisfaction as mediators of the relationship between weight status and being a victim of bullying

Research has found evidence of a link between being overweight or obese and bullying/peer victimisation, and also between obesity and adjustment problems such as low self-esteem and body dissatisfaction. Studies have also found that adjustment problems can put children at an increased risk of being bullied over time. However, to date the factors that place overweight or obese children at risk of being bullied have been poorly elucidated. Self-report data were collected from a sample of 11-14 year olds (N=376) about their weight status, about their experiences of three different types of bullying (Verbal, Physical and Social), their global self-worth, self-esteem for physical appearance, and body dissatisfaction. Overweight or obese children reported experiencing significantly more verbal and physical (but not social) bullying than their non-overweight peers. Global self-worth, self-esteem for physical appearance and body dissatisfaction each fully mediated the paths between weight status and being a victim of bullying.

Leader-member exchange and contextual performance:the mediating influence of organization-based self-esteem

This study examined the mediating influence of organization-based self-esteem (OBSE) on the relationship between leader-member exchange (LMX) and contextual performance. Respondents were Indian employees and their immediate supervisors. Results of structural equation modeling (SEM) that compared the fit of a fully mediated model to a partially mediated model revealed support for the hypothesized fully mediated model. Specifically, the SEM results showed the relationship between LMX and the contextual performance facets of interpersonal facilitation and job dedication to be indirect, through OBSE. Support for the hypothesized mediating influence of OBSE highlights the multiple motivational underpinnings of contextual performance

The development of maternal self-esteem

Although an important theoretical concept, little is known about the development of maternal self-esteem. This study explores the significance of maternal cognitions, psychopathological symptoms, and child temperament in the prediction of prenatal and postnatal maternal self-esteem. During pregnancy 162 women completed measures assessing their unhealthy core beliefs, psychopathological symptoms, and self-esteem. At 1 year postpartum 87 of these women completed measures assessing their self-esteem and their child's temperament. Overall maladaptive maternal core beliefs and psychopathological symptoms during pregnancy explained 19% of the variance in prenatal maternal self-esteem. Forty-two percent of the variance in maternal self-esteem at 1 year could be explained by a combination of prenatal maternal self-esteem, mental health symptoms, maternal core beliefs, and more unsociable infant temperament. Underlying maternal cognitive structures may be important in determining the development of maternal self-esteem. © 2007 2006 Michigan Association for Infant Mental Health.

Typical performance of regular low-density parity-check codes over general symmetric channels

Typical performance of low-density parity-check (LDPC) codes over a general binary-input output-symmetric memoryless channel is investigated using methods of statistical mechanics. Relationship between the free energy in statistical-mechanics approach and the mutual information used in the information-theory literature is established within a general framework; Gallager and MacKay-Neal codes are studied as specific examples of LDPC codes. It is shown that basic properties of these codes known for particular channels, including their potential to saturate Shannon's bound, hold for general symmetric channels. The binary-input additive-white-Gaussian-noise channel and the binary-input Laplace channel are considered as specific channel models.

Arlette Laguiller:does the mainstay of the French political far-left enjoy linguistic parity with her male counterparts?

While language use has been argued to reflect gender asymmetry, increasing parity has been evidenced in official settings (Holmes, 2000; Dister and Moreau, 2006). Our hypothesis is that the French national press has developed a norm of equal linguistic treatment of men and women. In a corpus of articles from Libération, Le Monde, and Le Figaro, we examine the treatment of Arlette Laguiller, the female leader of the French extreme-left 'Worker's Struggle' Party (Lutte Ouvrière), during the run-up to the 2007 presidential elections. How Laguiller is referred to and described in comparison with her male counterparts evidences no asymmetry. Breaches to parity are only found in the right-wing Figaro newspaper. The ideological distance between the newspaper and the candidate suggests that power struggles are a primary source of asymmetrical treatments. The discursive functions of such treatments can be understood through an investigation based on a portable corpus linguistics methodology for the measure of discrimination. © 2011 Elsevier B.V.

Statistical mechanics of mutual information maximization

An unsupervised learning procedure based on maximizing the mutual information between the outputs of two networks receiving different but statistically dependent inputs is analyzed (Becker S. and Hinton G., Nature, 355 (1992) 161). By exploiting a formal analogy to supervised learning in parity machines, the theory of zero-temperature Gibbs learning for the unsupervised procedure is presented for the case that the networks are perceptrons and for the case of fully connected committees.

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 method, errors occur, either when the information transmission is corrupted by atypical noise, or when multiple typical sequences satisfy the parity check equation as provided by the received corrupted codeword. We show that the average error rate for the second type of error over a given code ensemble can be accurately evaluated using the replica method, including the sensitivity to message length. Our approach generally improves the existing analysis known in the information theory community, which was recently reintroduced in IEEE Trans. Inf. Theory 45, 399 (1999), and is believed to be the most accurate to date. © 2002 The American Physical Society.