Design of highly parallel linear digital circuits based on symbol-level redundancy

In the non-linear digital system, it is difficult to design systematically highly parallel digital circuits whose output digit depends on a small number of input digits. On the other hand, the concept of linearity in digital systems is very attractive because analytical methods can be utilized to design highly parallel circuits. One of the most important problems in the design is to transform an original specification to a linear one. The design method of highly parallel circuits based on a necessary condition has been discussed. However, we cannot always find the solution even if the necessary condition is satisfied. To solve the problem, a sufficient condition for linearity is derived. If the sufficient condition is satisfied, we can design the linear circuit from the specification by the use of multiplicated redundant symbols.