Advanced study and research in this field deals with the encoding, transmission, retrieval, and interpretation of information in many forms. Students may pursue programs of study focusing on mathematical foundations, improved algorithms, and hardware/software implementation. Communications research focuses on the transmission of information over wireless, optical, and wired channels. Telecommunications engineering creates wired and wireless systems that satisfy desirable societal, bandwidth, and hardware constraints. Research in statistical communications aims at reducing adverse effects on signal transmission in such systems through probabilistic modeling. The channels considered range from subminiature networks inside a computer chip to broadband cable and communications satellites.<br><br>Information processing addresses the theory and engineering design associated with interpreting and manipulating received data, primarily in discrete form. Information theory and rate-distortion theory provide the foundation for a quantitative understanding of the nature and meaning of information. These theories treat the fundamental limits and algorithms for saving memory and bandwidth and protecting against transmission errors, such as in network coding.<br><br>Signal processing considers the application of digital processing techniques to problems encountered in many areas, including biomedical instrumentation, remote sensing, subsurface sensing and imaging systems, control systems, and audio processing. Special laboratories are available for speech processing, video and image processing, networking, communications, and document image analysis.