Progress in Mathematics for Communication Systems
Even though mathematics is accepted as core contributor to communication systems, the mathematics and engineering communities are historically not as well tied as, for example mathematicians and physicists. On the other side, the rapid development of new and more involved information and communication technologies necessitates a significant amount of mathematical content. Our summer academy attempts to outline the relations of these communities and help to direct young researchers of either groups into this growing interdisciplinary field.
For example, recent demands in high data rate and wireless communication systems have necessitated refining the mathematical tools and the development of new methods. Furthermore, these needs have led and continue to lead to difficult and interesting mathematical questions, some of which are currently addressed by both mathematicians and engineers, as well as from the scientific research and the industrial development point of view. It is worth mentioning, that some of the new ideas from engineers cross borders within the realm of communications, for example, the idea to achieve modulation and channel coding in a single processing step.
Our summer academy addresses some research on multi carrier modulation, turbo and LDPC codes and combinatorial optimization from the scientific and industrial and from the mathematical and engineering points of view.
Less well known is the other half of the mathematics / engineering cross-fertilization, namely, the mathematical results and theories that have been motivated by engineering problems. For example, questions from wireless communications have acted as starting points for research contributions to the mathematical theory of pseudo-differential operators.
The summer academy should lead to working relationships between the participating scientists representing both disciplines in equal numbers. The ratio of participants from universities to participants from industry is expected to be four to one.
Summer academies are a central mean of the International Center for Transdisciplinary Studies (ICTS) at Jacobs University Bremen to attract young scientists on the doctoral candidacy and post-doctoral level to join the center and its mission to promote interdisciplinary research activities on a local, national, and international level.
An interdisciplinary education is regarded to be of vital importance for science in the 21st century. It is often overseen though, that such education requires a significant dedication and risk from young scientists: after reaching research maturity in one discipline, they often experience immediate pressure to publish in their field in order to justify their role in the academic system. The study of the language and the methods of a second discipline is either delayed indefinitely or carried out at a later point of a scientist’s career. We believe that “languages should be learned as early as possible” and hope to contribute to this through our summer academy.
The two-week summer academy on Progress in Mathematics for Communication Systems is intended to serve young scientists from the disciplines of Electrical Engineering and Mathematics, both of which often differ substantially in language and scientific culture. Therefore, the courses offered at our ICTS summer academy include basic material in applied harmonic and functional analysis, probability theory, optimization, and finite fields which are taught by mathematicians, as well as basic material in coding theory, multi-carrier modulation, and wireless systems, contributed by electrical engineers. This will solidify the understanding of young scientists in their own discipline and provide insights into central topics, methods, concepts, and, last but not least, the language in the foreign discipline. These fundamental courses form the educational core of our summer academy.
Mathematical content and communications engineering aspects will be presented in alternating sections. The content between sections will be coordinated closely.
For example, the introduction into finite fields presented by a mathematics professor is followed by their applications in standard block codes, like Reed-Solomon or BCH codes. In the same way, stochastics and information theory, also given by a mathematician delivers the foundations for Turbo and LDPC codes. On the other hand, problems stemming from the time-varying nature of mobile communication channels have lead to new results in the theory of pseudodifferential operators. Similar groupings determine the design of the core education within our summer academy. Sometimes, it will even appear not too obvious any more, if an engineer or mathematician should be representing a certain topic. One of the learning goals will exactly be realizing the strong interconnection and placement of current communications research on the borderlines between “pure” mathematics and electrical engineering.
The structure of our summer academy includes also plenary lectures by international experts on current research results and future trends as central component. Current areas of active research that will be discussed include Gabor analysis, sparse approximations, Turbo, and Fountain codes, and multiple-input multiple-output wireless communications. Moreover, we reserve a small number of lectures for a discussion of future trends in these disciplines and the industrial perspective on the current and future necessities for communication systems.
Each lesson in the core course program will last 75 minutes and is followed by 15 minutes of discussion.
Participating young scientists will contribute a talk or a poster, those participants without already defined research orientation will be assigned an advisor who will design a project topic for the participant to work on while visiting the ICTS.
Further, we will try to allow ample time for discussions among participants and group and self study by the participants.
Participants are intended to leave Jacobs University not only with a sound understanding of some of the basic mathematical concepts in communications engineering and the long standing fruitful interaction of mathematics and communication systems, but foremost with knowledge of the mathematical and engineering problems that are currently examined on both sides of the aisle in order to improve a variety of communications systems. As importantly, participants will have made a step towards becoming scientists with an interdisciplinary research agenda.