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.

Self-esteem and job satisfaction of adults with mild mental retardation in sheltered workshops and supported employment programs

A sample of 200 adults with mild mental retardation were assessed on overall job satisfaction and self-esteem using the Vocational Program Evaluation Profile and the Coopersmith Self-esteem Inventory. The subjects worked either in a sheltered workshop or in a supported employment setting. Results indicated that there was a significant relationship between self-esteem and job satisfaction for both groups of subjects. In addition, subjects who worked in supported employment reported significantly higher levels of job satisfaction also. There was also an interaction between place of residence and place of employment when looking at self-esteem; those who live in a semi-independent home and work in supported employment reported the highest levels of self-esteem. These results are discussed in terms of the social validity of supported-employment for persons with mild mental retardation. ^

The effect of group counseling on the self-esteem, attendance, and counselor utilization of immigrant Hispanic secondary limited English proficient students

As the population of the United States becomes more diverse and the immigrant Hispanic, limited English proficient (LEP) school age population continues to grow, understanding and addressing the needs of these students becomes a pressing question. The purpose of this study was to investigate the effects of group counseling, by a bilingual counselor, on the self-esteem, attendance and counselor utilization of Hispanic LEP high school students. The design for this study was a quasi-experimental design. The experimental and control groups consisted of one class from each of the four levels of English for Speakers of Other Languages (ESOL), I-IV. The counseling intervention, the independent variable, was delivered by a bilingual counselor once a week, for fifteen weeks.^ A total of 112 immigrant Hispanic LEP students selected from the total ESOL student population participated in the study. The experimental and control groups were administered the Culture Free Self Esteem Inventory (CFSEI) Form AD as a pretest and posttest. The Background Information Questionnaire (BIQ) was utilized to gather information on counselor utilization and demographic data. Attendance data were obtained from the students' computer records. At the conclusion of the study the differences between the experimental and control groups on the three dependent variables were compared.^ Statistical analyses of the data were done using SPSS statistical software. A multivariate analysis of variance (MANOVA) was utilized to determine if there were significant differences in the self-esteem scores, attendance and counselor utilization. Correlational analyses was utilized to determine if there was a relationship between English language proficiency and self-esteem and between acculturation level and self-esteem.^ The study results indicate that there were no significant differences in the self-esteem scores and attendance of the subjects in the experimental group at the completion of the group counseling treatment. Counselor utilization was statistically significant for the targeted population. A relationship was found between English language proficiency level and self-esteem scores for students in ESOL levels II, III and IV. No significant correlation was found between acculturation and self-esteem.^ Research on the dropout rates of LEP coupled with the results of this study show that students at the intermediate and advanced levels of ESOL (III and IV) exhibit more positive self-esteem and achieve higher graduation rates that levels I and II. LEP students at levels I and II, once they became familiar with the role and function of school counselors through group counseling, utilized their services. ^