Error Control Codes, Parallel Processing, Computer Networks
My current research interests are in error control codes, parallel processing, and computer networks.
In the area of error correcting codes, we are developing codes that achieve zero error capacities in limited magnitude error channels. Both systematic and non-systematic optimal codes are designed. Errors in multi-level flash memories, m-PSK, etc. can be modelled using limited magnitude error channel. We are also developing t-error correcting codes for limited magnitude errors using the concept of elementary symmetric functions. In addition, we have been developing efficient codes for unidirectional/asymmetric errors. Simple and efficient design of encoder/decoder algorithms are also being studied. The other area that we have been studying is on the efficient design methods for balanced codes, where each code word contains equal number of 1's and 0's.
In the area of parallel processing, some new types of efficient interconnection networks based on the number theory concepts – Gaussian and EJ integers are being developed. The multi-dimensional Gaussian Networks have much better topological properties that of toroidal networks. Efficient design of communications algorithms, mapping algorithms, etc., with or without some faulty nodes in different networks are some of the research problems that we are currently investigating. Furthermore, using coding theory, some topological properties of different networks are being developed.