Clustering for Designing Error Correcting Codes

Acknowledgements I had the great pleasure of working with Dr. Anamitra Makur during my stay at the Institute. But for him, this thesis would not have seen light. I would like to thank him for the help he has rendered during this work. Suryan for their help. Jyothish and Jemlin for making my stay at the Institute a happy and memorable one. P r a h h and Mala who had been always helpful to me. Finally I would like to thank my parents for their constant encouragement throughout the course. Abstract In this thesis we address the problem of designing code1 fo; specific applications. To do so we make use oft he relationship bet ween dus ten and codes. Designing a block code over any finite dimensional space may be thought of as forming the corresponding number of elnsters over the par titular dimensional space, In literature we have a numb w of algorithms available for clustering. We have examined the performance of a number of such algorithms, such a Linde BuzbGr ay, Simnlat ed Annealing, Simulated Annealing wi th LindeJIuzb Gray, Det erminstie Annealing, ete, for design of codes, But dl these dgori t hmms make use of the Eucledian squared error distance measure for clustering. This di ~t ant ana measure does not match with the dist ance measure of intere~t in the error correcting scenario, namely, Hamming distance. Consequently we have developed an algorithm that can be used for clustering wi ti Hamming dis t a m as the distance measure, Also, it has been observed that stochastic algorithms, such as Simulated Annealing fail to ploduee optimum codes due to very slow convergence near the end. As a remedy, we havt proposed a modjfieation based on the code structure, for such algorithms f or code design whi ch makes it possible to converge to the optimum eodea