Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithms

Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iterative message passing. Concepts from mathematical programming used in the context of decoding include linear, integer, and nonlinear programming, network flows, notions of duality as well as matroid and polyhedral theory. This survey article reviews and categorizes decoding methods based on mathematical programming approaches for binary linear codes over binary-input memoryless symmetric channels.Comment: 17 pages, submitted to the IEEE Transactions on Information Theory. Published July 201

STRATEGI BIMBINGAN KELOMPOK MELALUI TRAINING GROUP DALAM PENGEMBANGAN INTEGRITAS AKADEMIK SISWA

Siswa dengan integritas akademik rendah cenderung untuk melakukan pelanggaran akademik dan menganggap pelanggaran akademik menjadi hal biasa. Penelitian ini bertujuan untuk menguji keefektifan strategi bimbingan kelompok melalui training group dalam pengembangan integritas akademik siswa. Metode yang digunakan adalah metode eksperimen dengan desain non equivalent pretest-posttest control group design. Partisipan penelitian berjumlah 24 orang (12 kelompok eksperimen dan 12 kelompok kontrol) yang dipilih secara purposive pada siswa yang memiliki integritas akademik rendah. Instrumen penelitian berupa angket integritas akademik siswa. Data dianalisis menggunakan uji perbedaan (U-Mann-Withney) dengan membandingkan rerata skor pada kelompok eksperimen dan kelompok kontrol. Hasil penelitian menunjukkan strategi bimbingan kelompok melalui training group cukup efektif dalam pengembangan integritas akademik siswa. Kata Kunci : Integritas Akademik, bimbingan kelompok, training group Students who had low academic integrity tend to commit academic violations and consider academic violations to be commonplace. This study aims to test the effectiveness of group guidance strategies through group training in developing students' academic integrity. The method used is an experimental method with a non equivalent pretest-posttest control group design. The number of participants in this study 24 students (12 experimental groups and 12 control groups) selected by purposive from students who had low academic integrity. The instrument used in this study is the academic integrity scale for students. Data were analyzed using the difference test (U-Mann-Whitney) by comparing the mean scores in experimental group and control group. Test results showed the group guidance strategy through group training was quite effective in developing students' academic integrity. Key Word : Academic Integrity, Group Guidance, Training Grou

Efficient Maximum-Likelihood Decoding of Linear Block Codes on Binary Memoryless Channels

In this work, we consider efficient maximum-likelihood decoding of linear block codes for small-to-moderate block lengths. The presented approach is a branch-and-bound algorithm using the cutting-plane approach of Zhang and Siegel (IEEE Trans. Inf. Theory, 2012) for obtaining lower bounds. We have compared our proposed algorithm to the state-of-the-art commercial integer program solver CPLEX, and for all considered codes our approach is faster for both low and high signal-to-noise ratios. For instance, for the benchmark (155,64) Tanner code our algorithm is more than 11 times as fast as CPLEX for an SNR of 1.0 dB on the additive white Gaussian noise channel. By a small modification, our algorithm can be used to calculate the minimum distance, which we have again verified to be much faster than using the CPLEX solver.Comment: Submitted to 2014 International Symposium on Information Theory. 5 Pages. Accepte

On a Cardinality Constrained Multicriteria Knapsack Problem

We consider a variant of a knapsack problem with a fixed cardinality constraint. There are three objective functions to be optimized: one real-valued and two integer-valued objectives. We show that this problem can be solved efficiently by a local search. The algorithm utilizes connectedness of a subset of feasible solutions and has optimal run-time

Efficiently Constructing Convex Approximation Sets in Multiobjective Optimization Problems

Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the approximation set up to a multiplicative factor in each component, a convex approximation set only requires this multiplicative approximation to be achieved by some convex combination of finitely many images of solutions in the set. This makes convex approximation sets efficiently computable for a wide range of multiobjective problems - even for many problems for which (classic) approximations sets are hard to compute. In this article, we propose a polynomial-time algorithm to compute convex approximation sets that builds upon an exact or approximate algorithm for the weighted sum scalarization and is, therefore, applicable to a large variety of multiobjective optimization problems. The provided convex approximation quality is arbitrarily close to the approximation quality of the underlying algorithm for the weighted sum scalarization. In essence, our algorithm can be interpreted as an approximate variant of the dual variant of Benson's Outer Approximation Algorithm. Thus, in contrast to existing convex approximation algorithms from the literature, information on solutions obtained during the approximation process is utilized to significantly reduce both the practical running time and the cardinality of the returned solution sets while still guaranteeing the same worst-case approximation quality. We underpin these advantages by the first comparison of all existing convex approximation algorithms on several instances of the triobjective knapsack problem and the triobjective symmetric metric traveling salesman problem

Brand Equity As An Interveing Variable In The Relationship Between Celebrity Endorser And The Firm’s Performance Of Medan City Cakes

This research aims to analyze the celebrity endorser on the performance of the Medan City cakes through brand equity as an intervening variable. The target population of the researcher is all people of Medan City who have bought one or more Medan City cakes, such as: Medan Napoleon, Medan Par Par, Bolu Toba Medan and Medan Mulaka at outlets/stores so the number can never be known. The research sample used 300 people, namely the people of Medan City who had bought one or more Medan City cakes, such as: Medan Napoleon, Medan Par Par, Bolu Toba Medan and Medan Mulaka at outlets/stores through the simple random sample method. The hypothesis tested in this study used the t value test. From the results of the tests that have been carried out, it can be obtained that the celebrity endorser variable on the firm performance variable through the brand equity as an intervening variable is a positive and significant relationship. Celebrity endorsers should reflect the company's value and it is hoped that celebrity endorsers will continue to improve their performance so that it creates trust and strong attraction by target consumers and can increase the brand equity of Medan City cakes