**White Paper**

# Comprehensive statistical analysis of SERDES links considering the effect of DFE error propagation

## Introduction and overview

As the speed of digital transmission increases, the links operate at their margins defined by the channel loss, reflections, jitter, crosstalk, noise and other impairments. For this reason, designers use all available equalization schemes to improve the signal to noise ratio at the receiver output. DFE (decision feedback equalizer) is one of the important equalization instruments. Unlike linear equalization (FFE and CTLE), it provides a feedback signal to eliminate inter-symbol interference associated with already detected symbols. However, if the detected symbol is wrong, the feedback is no longer the desired signal, and it can increase the probability of subsequent errors. This leads to so-called DFE error propagation or burst error.

The paper is organized as follows. Sections II-IV define the essential building blocks of the statistical solver. In section II we provide definitions of the main elements of the statistical analysis and compare the single bit/pulse response-based approach with the incremental transitions approach. Section III introduces the “convolution term”, the new element of the statistical solver that includes various types of DFE feedback. Section IV defines symbol error probability matrix and its use when building statistical convolution terms. The flow that finds the BER/SER metrics of the channels in presence of DFE error by iterations is defined in section V. Section VI discusses the use of the modified iteration process to find the probability distribution of symbol error groups, and section VII describes the experimental study of the statistical solver.