A Matrix-Based Method for Fast and Memory-Efficient Statistical Eye Diagram Generation

Abstract This paper proposes a computationally efficient method for generating statistical eye diagrams using a matrix-based approach, tailored for high-speed SerDes communication systems. Unlike traditional convolution-based methods, which suffer from high computational complexity and memory demands, the proposed technique leverages matrix multiplication to model all inter-symbol interference (ISI) combinations. The method introduces an optimized chunk-based matrix segmentation strategy that reduces memory usage, and it exploits data-level parallelism to significantly enhance runtime performance. Experimental results demonstrate a simulation time reduction from over 1000 seconds to just 1.5 seconds while maintaining high accuracy in bit error rate (BER) estimation. This approach enables precise, scalable, and memory-efficient analysis of signal integrity, making it suitable for advanced high-speed digital system design.