Tree-Based Construction of LDPC Codes Having Good Pseudocodeword Weights

We present a tree-based construction of LDPC codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a $d$-regular tree for a fixed number of layers and employing a connection algorithm based on permutations or mutually orthogonal Latin squares to close the tree. Methods are presented for degrees $d=p^s$ and $d = p^s+1$, for $p$ a prime. One class corresponds to the well-known finite-geometry and finite generalized quadrangle LDPC codes; the other codes presented are new. We also present some bounds on pseudocodeword weight for $p$-ary LDPC codes. Treating these codes as $p$-ary LDPC codes rather than binary LDPC codes improves their rates, minimum distances, and pseudocodeword weights, thereby giving a new importance to the finite geometry LDPC codes where $p > 2$.Comment: Submitted to Transactions on Information Theory. Submitted: Oct. 1, 2005; Revised: May 1, 2006, Nov. 25, 200

Employability of the Graduates From 14 CFR PART 147 Schools: Understanding the Critical Factors Using Covariance-Based SEM

Certified aviation mechanics are crucial to maintaining a healthy aviation industry in the United States. To fulfill this need, 14 CFR Part 147 aviation mechanic schools educate students under the supervision of the FAA. Though the demand for mechanics is projected to increase over the next 20 years, the supply is not expected to meet this demand. Therefore, the research discussed in this paper addressed this potential deficiency by asking two research questions. The first related to the factors students feel affect their employability, and the second was used to analyze whether the students learned these skills at school or through personal development. To address the research questions, a Q-sort was conducted with recruiters in the industry. The recruiters organized 19 factors, which the researcher chose during the literature review, in order of importance to the industry. The 11 factors that rated the highest were then placed in a survey. Questions for each factor were chosen from published scales and combined into a survey that was administered in person and online. After data cleansing, 210 records were used in the model. The first step of the analysis was to complete a confirmatory factor analysis in AMOS. The factors used in the model for the first question were the top four from the Q-sort results: technical skills, problem solving, reliability, and teamwork. The model fit was excellent, with a CFI of .977, TLI equal to .969, and RMSEA of .041. The covariance-based structural equation model (SEM) was then executed. Among all participants, none of the factors had a significant impact on self-perceived employability. However, after separating the data between participants who were employed and unemployed, the model was adjusted and the model fit maintained excellence. The new SEM analysis showed employed graduates felt problem solving significantly affected their employability. In contrast, unemployed students felt reliability significantly affected their employability. For the second research question, the SEM analysis for combined employed and unemployed participants showed the critical skills for employability were being taught in 14 CFR Part 147 schools after model fit statistics of .918 CFI, .907 TLI, and RMSEA of .067 were found in the CFA. Once the data were separated into unemployed and employed participants, the employed group measured a significant and positive effect on the employability-critical skills being taught in the mechanic schools, whereas the unemployed participants did not. All three groups resulted in a nonsignificant effect of personally developed skills. These results are critical for industry leaders to understand and incorporate into the education of aviation mechanics. Employability studies have been conducted in the business field for decades to understand and return the unemployed to employment. In the realm of education, results can help school leaders teach their students which factors are critical to employers and ensure these skills are highlighted in the curriculum. Within the aviation industry, this information can be used to address the growing gap between the supply and demand of qualified mechanics. If actions are not taken over the next few years, adverse effects, such as canceled flights, delayed deliveries, and increased costs will be felt throughout the industry

Algebraic Design and Implementation of Protograph Codes using Non-Commuting Permutation Matrices

Random lifts of graphs, or equivalently, random permutation matrices, have been used to construct good families of codes known as protograph codes. An algebraic analog of this approach was recently presented using voltage graphs, and it was shown that many existing algebraic constructions of graph-based codes that use commuting permutation matrices may be seen as special cases of voltage graph codes. Voltage graphs are graphs that have an element of a finite group assigned to each edge, and the assignment determines a specific lift of the graph. In this paper we discuss how assignments of permutation group elements to the edges of a base graph affect the properties of the lifted graph and corresponding codes, and present a construction method of LDPC code ensembles based on noncommuting permutation matrices. We also show encoder and decoder implementations for these codes

Algebraic Design and Implementation of Protograph Codes using Non-Commuting Permutation Matrices

Random lifts of graphs, or equivalently, random permutation matrices, have been used to construct good families of codes known as protograph codes. An algebraic analog of this approach was recently presented using voltage graphs, and it was shown that many existing algebraic constructions of graph-based codes that use commuting permutation matrices may be seen as special cases of voltage graph codes. Voltage graphs are graphs that have an element of a finite group assigned to each edge, and the assignment determines a specific lift of the graph. In this paper we discuss how assignments of permutation group elements to the edges of a base graph affect the properties of the lifted graph and corresponding codes, and present a construction method of LDPC code ensembles based on noncommuting permutation matrices. We also show encoder and decoder implementations for these codes

Evaluation of COVID-19 on AMT Part 147 Schools Related to Knowledge-based Testing Scores for AMG, AMA, & AMP Mechanic Certification Examinations

The FAA mandates under CFR 14, Part 65 Subpart D § 65.75 Knowledge requirements, that an applicant for a mechanics certificate must possess. The knowledge-based test, more commonly referred to as the “written” examinations and covers materials specific to either an airframe certificate (AMA) or a powerplant certificate (AMP) with the general (AMG) component being common to each. The prescribed level of testing for a Part 147 school is specifically outlined under § 147.38a Quality of instruction and measured by the results of the KBT examinations for all students tested and measured against a national norm. During the period of COVID both training and learning challenges have taken place throughout the system of approved institutions. This paper investigates standardized national norm scores at a pre-pandemic level and compares them to the time frame of the results during the actual pandemic using data from March 2020 up to the current period. Data gathered from the FAA Form 8080-08 collected by AFS630 was reviewed and analyzed and stratified by institution, regions, and students. A noticeable drop in the national scores and the individual scores related to each of the three testing regimes, AMG, AMA, and AMP of all the accredited schools was documented. This research endeavors to draw possible conclusions as to the underlying fundamental reasons for the phenomena as discussed, offering both insight and possible corrective actions to be considered