Design of three high-performance concurrent systolic arrays for band matrix multiplication

Band matrix multiplication is widely used in the concurrent system. But traditional Kung-Leiserson systolic array for band matrix multiplication cannot realize high cell efficiency because only about 1/3 cells are operated in each step. Thus three alternative designs are presented based on the ideas of "Matrix compression" and "Super pipelined". These new arrays arrange and compress the data matrix skillfully, and add the Processing elements (PE) or readjust the operation sequence to increase the cell efficiency. These changes realize higher cell efficiency and faster operation speed with more intricate architectures. The results show that the best systolic array for band matrix multiplication can use almost 100% processing elements in each step, which is nearly triplication of the traditional Kung-Leiserson system. Also, these modifications increase the operation speed and at best spend only 1/3 processing time to complete the multiplication operation.