Coding for efficient information transmission in optical and wireless systems

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The long-term research program supported by this award is focused on devising efficient encoding and decoding techniques for reliable information transmission over a variety of channel-types, including wireless channels, optical channels, and packet-network channels. The challenge is to achieve coding schemes that (a) have an efficiency approaching information-theoretic limits; and (b) can be encoded and decoded with practical algorithms. Research challenges arise because different channels often require quite different approaches. It becomes essential to achieve a good understanding of the operation of the channel, both to establish fundamental limits and to construct the most suitable coding schemes. Since error-control coding is a central component of every modern communications system, this work has the potential to improve the efficiency of existing and emerging communications systems, giving service-providers a competitive advantage, and giving their users better (cheaper, faster, more reliable) service. Three sub-projects are aimed at achieving this long-term objective. One of them targets highly dynamic wireless multi-hop or mesh networks that arise in public safety, disaster recovery, and tactical radio scenarios. Another targets the efficient transmission of information over optical fibers using a novel approach based on the Inverse Scattering Transform. The third aims to examine the properties and applications of a new class of error-correcting codes based on non-commutative skew polynomial rings. In all cases, the training of people (from undergraduate students, to graduate students, to postdoctoral fellows) is given significant emphasis.