9457509, PI-Mitchell D. Trott: The award will support two projects. The first project integrates and extends results from algebra, system theory, symbolic dynamics, and coding theory to develop a structural framework for the analysis and synthesis of nonlinear trellis codes. Trellis codes, introduced by Ungerboeck in 1982, are used in essentially all modern voice-band modems; the recent V.34 ITU modem standard specifies three types of trellis codes that achieve communication rates exceeding 28800 bits per second over ordinary telephone lines. Despite the continued interest in their construction, no comprehensive theory of trellis codes has emerged. The trellis codes specified in current and proposed standards, for example, were designed largely via ad hoc pencil-and-paper heuristics and computer search. These methods have reached their complexity limit, and future codes, with 256 states or more, must be found by other means. The aim of this project is to use systems over groups to describe the symmetries inherent in good codes, thereby facilitating the analysis of existing codes and the construction of new ones. The second research project will develop results in multiple access communication. There has been a recent explosion of interest in wireless voice, video, and data communication over newly allocated radio bands. The multiple access communication environment in these bands is characterized by fading, multipath, and non-Gaussian noise. Intuit ion and rules of thumb for point-to-point communication over Gaussian channels is often misleading when applied to this new environment. The goal of the project is to develop a new intuition appropriate to radio. This will require both a deeper theoretical understanding of the fundamental performance limits of the channel and also an understanding of how information-theoretic results can be translated into practical implementations. Specific subproblems include optimal detection, adaptive antenna algorithms, and multiple access coding techniques, especially as applied to communication at rates 1 Mb/sec or more.
