Frames from first principles: Error correction, symmetry goals, and numerical efficiency (09w5082)


Bernhard Bodmann (University of Houston)

(University of Missouri)

Gitta Kutyniok (LMU Munich)

Ozgur Yilmaz (University of British Columbia)


The Banff International Research Station will host the "Frames from first principles: Error correction, symmetry goals, and numerical efficiency” workshop next week, March 15 - March 20, 2009.

Digital signal transmissions have revolutionized our daily lives, from cellular phones and Voice-over-Internet-Protocol telephony to High-Definition Television and other streaming media. The use of digitization guarantees seemingly faultless communication by repeating information in the stream of transmitted bits and bytes. However, at times the digital nature of error suppression leads to behaviors that do not resemble the graceful degradation we recall from analog technology. Such problems could range from blocky images, choppy satellite radio, or dropped cell-phone calls to possible instabilities in digital fly-by-wire control systems.

This undesirable behavior can be caused by imperfections in the digitization process or by transmissions using digital error-correction schemes which are not tailored to the type of the transmitted signal, say audio or video. Understanding the best way to use repeated information in the digitization as well as in the transmission processes seems the key to significant progress in this field. Engineers have already contributed many approaches to address this challenge, which lead to interesting mathematical questions. Answering these questions as well
as developing a systematic treatment for digital transmissions is a primary motivation for this workshop.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí­a (CONACYT).