# Mathematical Coding Theory in Multimedia Streaming (15w5150)

Arriving in Banff, Alberta Sunday, October 11 and departing Friday October 16, 2015

## Organizers

(University of Kentucky)

(University of Toronto)

(University of Zurich)

(Bell Labs Research)

## Objectives

Emerging multimedia applications require error correction codes that have very different properties from classical codes. Researchers working in this field have made progress in recent years in finding abstractions of such systems that are realistic, yet analytically tractable. However the error correction codes, such as those discussed in Subtopic~2, have been developed from first principles in specific settings. There is no general theory till date for such constructions. On the other hand researchers working on convolutional codes in recent years have made a significant progress on the dynamical systems theory underlying these constructions without a particular emphasis on multimedia systems. A primary objective of the workshop is to bring together researchers working in these two areas to combine their knowledge and develop a general theory for constructing streaming codes that can be implemented in future multimedia systems. We therefore expect about half of the participants to be experts in coding theory, and many of them will be from applied mathematics departments worldwide. The remaining half of the participants will be communication theorists working on engineering systems. Banff therefore provides an ideal venue for this workshop, and there does not appear to be another similar venue where such a workshop can be organized.To achieve our proposed objective the workshop will have the following components:
• A series of 1/2 hour talks aimed to disseminate recent research results.
• In the area of multimedia systems both theoretical investigations and experimentally oriented results will be presented. In coding theory, recent progress on both faster encoding and decoding techniques, as well as fundamental bounds will be presented.
• A small number of longer tutorial style talks, where participants are exposed to classical results in convolutional codes, information theoretic limits of multimedia streaming, as well as lessons learned from real-world implementations.
• An open problem session. Existing results on streaming codes will be re-examined using the framework of convolutional codes, and powerful techniques from dynamical systems theory will be used to tackle some open problems involving streaming codes in ~cite{streaming-1} and elsewhere.
Relevance: While coding theory has many important engineering applications, it has also evolved independently as a branch of applied algebra. This workshop will introduce researchers in coding theory in general, and convolutional coding in particular, to some emerging problems in multimedia communication systems. By introducing the relevant source and channel models used in such systems, and discussing some key toy problems," the proposed workshop will expose researchers to a new, stimulating class of research topics that have not been considered before. Likewise researchers working on multimedia streaming will be exposed to new metrics for error correction codes, beyond classical distance, relevant to streaming communications. Importance: Video already accounts for over 50% of the internet traffic today in both wired and wireless networks. Mobile video traffic is expected to grow by a factor of more than $20$ in the next five years~cite{cisco}. To satisfy such an explosive growth it is crucial to develop highly efficient communication techniques. Application layer forward error correction has already been considered by a number of standardization committees, such as 3GPP and DVB, and is being implemented in systems such as eMBMS. By applying the deep understanding of convolutional codes developed in the mathematics literature to problems of current engineering relevance in multimedia systems, the proposed workshop is expected to have a significant impact on both communities.Timeliness: While error correction codes for reliable communication have been studied for several decades, coding theory for low-latency, real-time, streaming systems is a fertile area of research. In contrast to classical codes that can use long block-lengths to exploit the average statistics of the channel, codes for streaming systems must inherently have a convolutional structure. They must be based on the local dynamics of the communication channel, and be designed for very different metrics than classical codes. Such properties have only been discovered in the last few years by researchers working in coding theory and communications systems. Therefore it is very timely to cross-fertilize the efforts of these communities and develop a general mathematical framework for error correction codes for multimedia applications.