BEE: Predicting realistic worst case and stochastic eye diagrams by accounting for correlated bitstreams and coding strategies

Modern high-speed links and I/O subsystems often employ sophisticated coding strategies to boost error resilience and achieve multi-Gb/s throughput. The end-to-end analysis of such systems, which involves accurate prediction of worst-case and stochastic eye diagrams, is a challenging problem. Existing techniques such as Peak Distortion Analysis (PDA) typically predict overly pessimistic eye diagrams because they do not take into account the coding strategies employed. Monte-Carlo methods, on the other hand, often predict overly optimistic eye diagrams, and they are also very time-consuming. As an alternative, we present BEE, an accurate and efficient computational technique that applies dynamic programming algorithms to predict realistic worst-case and stochastic eye diagrams in modern high-speed links and I/O subsystems - with neither excessive pessimism nor undue optimism. BEE is able to fully and correctly take into account many features underlying modern communications systems, including arbitrary high-level transmit-side coding schemes and strategies, as well as various low-level non-idealities introduced by the underlying channel(s), such as inter-symbol interference (ISI) and crosstalk, asymmetric rise/fall times, jitter, parameter variability, etc. Furthermore, BEE accurately captures the fact that different received bits typically have widely different eye diagrams when a channel is driven by correlated bitstreams generated by coding strategies. We demonstrate BEE on links involving (7,4)-Hamming and 8b/10b SERDES encoders, featuring channels that give rise to multiple reflections, dispersion, loss, and overshoot/undershoot. BEE successfully predicts actual worst case eye openings in all these real-world systems, which can be twice as large as the eye openings predicted by overly pessimistic methods like PDA. Also, BEE can be an order of magnitude faster (and much more reliable) than Monte-Carlo based eye estimation methods.