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SCIENCE CHINA Information Sciences, Volume 63, Issue 6: 160406(2020) https://doi.org/10.1007/s11432-019-2848-3

Deep belief network-hidden Markov model based nonlinear equalizer for VCSEL based optical interconnect

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  • ReceivedDec 15, 2019
  • AcceptedMar 18, 2020
  • PublishedMay 11, 2020

Abstract

The data center has developed rapidly over the past few years, leading to the demand for high speed data transmission. Vertical cavity surface emitting lasers (VCSELs) based optical interconnect is evolving to 100 Gb/s and beyond, which makes nonlinear distortions difficult to be compensated or equalized by conventional equalizers. Moreover, the challenge becomes very complicated for conventional equalizers because of the presence of inter-symbol interference (ISI) together with the nonlinear distortions. So many neural network based DSP algorithms such as artificial neural network (ANN) have been proposed to mitigate the distortions. However, ANN has the limitations that sample's relevant information is not considered, leading to degradation in ANN's performance and high computational complexity. In this paper, in order to maintain an excellent capability of mitigating nonlinear distortions like other neural network based equalizers while considering the sample's relevant information to reduce the computational complexity, we propose a deep belief network-hidden Markov model (DBN-HMM) based nonlinear equalizer which is tested in a PAM-4 modulated VCSEL and multimode fiber (MMF) optical interconnect link experimentally. The BER performance can be greatly improved compared with conventional DSP algorithms. In addition, the computational complexity of DBN-HMM based equalizer can be about 41% lower than that of ANN based method with a similar BER performance.


Acknowledgment

This work was supported by National Key RD Program of China (Grant No. 2019YFB1802904) and Joint Fund of the Ministry of Education (Grant No. 6141A02033347).


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  • Figure 1

    (Color online) The pre-processing of signals, the current transmitted signal and its ${L}$ adjacent signals are mapped into a new symbol. For the received signal, the current vector after sinc interpolation and its ${L}$ adjacent vectors are wrapped as the final feature vector.

  • Figure 2

    (Color online) (a) The structure of RBM; (b) the structure of DBN, which can be approximated as the stack of RBMs.

  • Figure 3

    (Color online) The training process of DBN-HMM based equalizer. The dataset is divided into ${N}$ sub-datasets, ${\rm~DBN}^{(m)}$ is trained with the $m$th sub-dataset ($m=1,2,\dots,N$).

  • Figure 4

    (Color online) The equalizing process of DBN-HMM based equalizer.

  • Figure 5

    (Color online) Experiment block diagram of VCSEL based optical interconnect link with DBN-HMM. The input data is generated with bit-pattern generator (BPG) using random pattern (56 Gb/s).

  • Figure 6

    (Color online) Measured BER vs. ROP with different equalizing strategies. The adjacent number $L~=~2$, the BER performance of MLSE and ANN are also given. In ANN(8, 2, 20), 8, 2, 20 represent the interpolation multiple, adjacent number, and the number of neurons in hidden layer respectively. Compared with MLSE, the BER performance of DBN-HMM(8, 2, 15) can be greatly improved. DBN-HMM(8, 2, 15) and ANN(8, 2, 20) have the same computational complexity.

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