This research topic investigates several fundamental topics in coding theory as applied to reliable data communication. The major areas of study are: (1) codes with multi-level error- correcting capabilities, (2) weight distributions of linear block codes, (3) block coded modulation, and (4) coding techniques for error control. In the first area, codes are sought which can provide different levels of error protection for different parts of a message. An example of application is the broadcast channel where different receivers operate in different noise environments, hence requiring different levels of protection. The second research area is motivated by the need for simpler schemes to evaluate the error control performance of broader classes of codes. The third area addresses the problem of combined modulation and block coding to achieve highly reliable and bandwidth-efficient data communication systems. Similar techniques, but using trellis ( or convolutional) coding rather than block coding, have emerged as an important application in modern data systems ( especially for voice-band and satellite channels). The final area is the continued development of the idea of cascaded coding, which is a generalization of concatenated coding. This concept, in conjunction with the preceding topic, could lead the way to development of systems with extremely low error probability with a minimal increase in assigned channel bandwidth. In addition to suggesting specific solutions to current data transmission problems, this project is likely to lay the groundwork for future research in coding theory.
