Modeling And Analysis Of Channel Errors Based On Multi-Order Memory Markov Chains

With the wide application of 5G technology,in order to meet the needs of data transmission,high-speed I/O interfaces have higher and higher requirements for data transmission rates.Signal integrity problems such as reflection,loss,crosstalk,jitter,and noise seriously affect the stability of high-speed I/O interfaces,causing serious distortion of the received signal waveform,and cause error bits.In order to improve the reliability of data transmission,it is necessary to perform FEC coding on the transmitted data to improve the SNR.Signal integrity problems such as DFE error propagation seriously affect the error correction capability of FEC coding.In order to reduce the number of bit errors after FEC correction,it’s necessary to understand the channel characteristics and obtain the location of the bit errors.Although transient simulation technology can obtain the above information,for links with low bit error rate requirements(below 1e-12),the simulation time is too long,which is not suitable for providing coding guidance.Channel error modeling technology can predict the error level after FEC correction,so this technology is often used for coding work guidance.At present,the channel error modeling method commonly used in the engineering field only considers the influence of data non-correlated interference on the channel,and does not consider the influence of data correlation interference such as ISI.In the case of considering the interference of data correlation,how to quickly obtain the location of the bit error to guide the coding work has become a major difficulty.Based on the above problems,this paper proposes a Markov chain error modeling method based on N-UI memory.This modeling method can fully consider the impact of a series of data-dependent interference such as jitter and ISI.Due to the limited duration of ISI,the probability distribution of N groups of tails that are close to the main cursor with the influence of ISI can be superimposed on the probability distribution of the main cursor by convolution to obtain the probability of receiving data at the next moment.The transition matrix of the channel error model in this paper can predict the state of the transmitter and receiver at the next moment.The transition matrix is arranged according to a certain rule,which is beneficial to the aggregation of states and the observation of state changes.The channel error model is simulated by Markov chain Monte Carlo method.The Markov Chain Monte Carlo method characterizes the process of state walking in the transition matrix by generating a large number of samples.We can obtain information such as error locations from the generated samples to guide the coding work.In order to verify the accuracy of the channel error modeling,we compare the results of the transient simulation with the simulation results of the channel error model in this paper to verify the accuracy of the channel error modeling.For low bit error rate channel analysis,it’s usually necessary to simulate long data sequence.The Markov chain Monte Carlo method takes too long to simulate long sequences,which is not conducive to the study of channels with low bit error rates.Therefore,this paper proposes an acceleration algorithm based on the Markov chain Monte Carlo method,in which the short consecutive correct state transition process conforms to the Markov process,and the long consecutive correct state transition process conforms to the Bernoulli process.This method can greatly shorten the simulation time and further improve the practicability of modeling.By comparing the simulation results of the Markov Chain Monte Carlo method with the accelerated algorithm,and analyzing the probability of consecutive correct states and the number of consecutive incorrect states for the same simulation length,the accuracy and effectiveness of the method are verified.