ABSTRACT
In many signal processing and computing systems, one is faced with the task of processing data which is inherently defined in Z(M) or CZ(M), or can equivalently be converted to one. Such arithmetic is based on the number theoretic properties of data sequences. Along other lines, coding theory has flourished as an art and science to protect numeric data from errors, thereby improving the performance of data processing systems. However, by and large, with certain exceptions, coding theory is developed as it applies to digital communication systems. This is evident from a number of texts on coding theory as it relates to communication theory. Exception to this is the application of coding theory concepts to fault tolerant computing systems. With the advent of very large scale integration (VLSI) design methodology and concepts of parallel processing, there has been tremendous thrust towards high performance computing systems that possess fault tolerance capability. The original idea of algorithm based fault tolerance (ABFT) is based on some of the classical results available in coding theory.
