Mathematical Programming for Generalized Turbo Coding Schemes

Modern digital communication systems require reliable transmission of information. A message being sent via a noisy channel is typically disturbed before arriving at the receiver side. Thus, decoding methods are needed to restore the original information. The efficiency of these methods depends on the codes and the decoding algorithms employed. Efficient codes and algorithms allow for a high data rate with a negligible number of decoding errors in practice. For example, next generation wireless networks a re required to allow high-speed Internet access with mobile devices. Channel coding is the discipline of constructing codes and realizing suitable (de)coding algorithms. A seemingly unrelated field of science is mathematical optimization which certainly also impacts our everyday life, e.g., in transportation, manufacturing, and organization processes. Mathematical optimization typically centers around a mathematical model describing a real-world problem. Based on this, mathematics helps to analyze this m odel theoretically. This mathematical theory is then utilized in terms of solution algorithms for the practical problems at hand. In recent years, started by the work of Feldman et al. in 2005 on "Linear Programming Decoding of Binary Linear Codes", it w as recognized that both fields are strongly related on a theoretical level and can benefit from each other. One particular target of our research will be 3-dimensional turbo codes, a generalization of the ground-breaking class turbo codes, invented by Ber rou et al. in 1993. By bringing together researchers from the Selmer Center and the Optimization Research Group as well as the Microelectronic Systems Design Research Group of the University of Kaiserslautern in Germany, our aim is to contribute to this fruitful interdisciplinary area of research. This is especially promising since both teams have already worked in this area on different topics for years and thus gained notable experience therein.