Some Coding Techniques for VLSI and Computer Systems

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The proposal deals with some new classes of codes applicable to computer and VLSI system. New design methods for balanced codes, where each codeword contains equal number of 1's and 0's, and low weight codes are investigated. These codes find broad applications - reducing noise and conserving power in VLSI systems, maintaining data integrity in write-once memories, obtaining delay insensitive communications in asynchronous systems, data encoding in fiber optics, etc. New classes of higher radix and binary Gray codes are also investigated. In Gray code sequence, two consecutive codewords differ in one digit position by 1. Gray codes find applications in wide areas - analog to digital converters, data compression, graphics and image processing, hashing, efficient combinatorial algorithm design, processor allocation in the hypercube, solving puzzles such as towers of Hanoi, etc. Our goal is to find new methods for designing these codes. Some preliminary results and the future research efforts related to these topics are described.