Electrical Engineering Systems Seminar
In signal processing, transforms are typically employed for analyzing or compressing real- or complex-valued signals. If the transform is chosen appropriately, certain characteristics of the signal, such as spectral content or sparsity, become readily accessible in the transform domain. It is fair to say that such transforms access information in the signal indirectly through manipulation of energy. In contrast, in information-theoretic settings, information is processed directly by various transforms over finite fields, as in linear source or channel coding schemes. In this talk, we will follow the information-theoretic approach and focus on the evolution of entropy in the course of certain transforms over arbitrary number fields. In particular, we will try to identify conditions for entropy polarization---a phenomenon that has been useful in constructing capacity-achieving source and channel codes using a low-complexity transform over the binary field. We will comment on whether entropy polarization can be a useful tool for compression of signals over real and complex fields.