Design and Evaluation of a Power-Efficient Approximate Systolic Array Architecture for Matrix Multiplication

Matrix multiplication (MM) is a basic operation for many Digital Signal Processing applications. A Systolic Array (SA) is often considered as one of the most favorable architecture to achieve high performance for matrix multiplication. In this paper, the design exploration for an approximate SA is pursued; three design schemes are proposed by introducing approximation in multiple sub-modules. An approximation factor $\alpha$ is introduced; it is related to the inexact columns in the SA to explore the accuracy-efficiency trade-off present in the proposed designs. In the evaluation, an 8-bit input operand matrix multiplication is considered; the Synopsys Design Compiler at 45nm technology node is used to establish hardware-related metrics. The Error Rate (ER), Normalized Mean Error Distance (NMED) and Mean Relative Error Distance (MRED) are used as figures of merit for error analysis. Results show that the proposed architecture for 8-bit matrix multiplication with an approximation factor $\alpha=7$ has the lower power consumption compared to existing inexact designs found in the technical literature with comparable NMED. In addition, a power delay product vs NMED analysis shows the proposed designs have a lower PDP so applicable to low power applications. The practicality of the proposed architecture is established by computing the Discrete Cosine Transform.