Area efficient computing structures for concurrent error detection in systolic arrays

A method of designing testable systolic architectures is proposed in this paper. Testing systolic arrays involves mapping of an algorithm into a specific VLSI systolic architecture, and then modifying the design to achieve concurrent testing. In our approach, redundant computations are introduced at the algorithmic level by deriving two versions of a given algorithm. The transformed dependency matrix (TDM) of the first version is a valid transformation matrix while the second version is obtained by rotating the first TDM by 180 degrees about any of the indices that represent the spatial component of the TDM. Concurrent error detection (CED) systolic array is constructed by merging the corresponding systolic array of the two versions of the algorithm. The merging method attempts to obtain the self testing systolic array at minimal cost in terms of area and speed. It is based on rescheduling input data, rearranging data flow, and increasing the utilization of the array cells. The resulting design can detect all single permanent and temporary faults and the majority of the multiple fault patterns with high probability. The design method is applied to an algorithm for matrix multiplication in order to demonstrate the generality and novelty of our approach to design testable VLSI systolic architectures.This work has been supported by a grant from the Natural Sciences and Engineering Research Council of Canada.