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Spiking Neural Network-based Equalization and Demapping in IM/DD Systems: A Comparison

Eike-Manuel Edelmann, Alexander von Bank, Laurent Schmalen

arXiv:2609.36103v1eess.SP

TL;DR

ANN receiver complexity can make communication systems power-hungry, while SNN-based equalizers and demappers have shown promise for IM/DD links. This paper systematically compares their design choices and finds trade-offs across BER, spike activity, and model size, with decision feedback especially beneficial for links with more severe CD-induced ISI.

  • Problem

    Prior SNN equalizers and demappers differ in design choices and channel conditions, leaving their effects without a systematic comparison.

    Source: §I · p. 2

  • Method

    The paper compares decision feedback, recurrent connections, neural encodings, and regularization for SNN equalizers and demappers across IM/DD links.

    Source: §I · p. 2, §V · p. 12

  • Results

    For links with more severe CD-induced ISI, decision feedback can significantly improve BER; recurrent connections can also improve BER while increasing model size and spike activity.

    Source: H. Discussion · p. 11, §V · p. 12

  • Takeaways & Limitations

    Design choices trade off BER, average spikes per inference, and model parameters, so the preferred SNN configuration depends on application-specific goals.

    Source: §V · p. 12

    End-to-end energy efficiency remains to be substantiated on neuromorphic hardware, and digital encoding may add ADC/DAC power overhead.

    Source: H. Discussion · p. 11

Abstract

from arXiv · show

In recent years, artificial neural networks (ANNs) have emerged as the de facto standard for addressing challenging problems in communications engineering that are difficult to solve using traditional methods. However, the dense matrix multiplications employed in ANNs often result in high computational complexity and, consequently, power-hungry systems. To overcome these limitations, researchers are turning to alternative computational models, such as spiking neural networks (SNNs), which promise highly energy-efficient computation. Recent works have shown that SNN-based equalizers and demappers achieve promising results in non-coherent short-reach optical communication systems affected by chromatic dispersion and nonlinear distortion. However, the proposed approaches differ in several design choices, such as the incorporation of decision feedback, the use of recurrent connections inside the SNN, different neural encodings, and regularization techniques. A systematic comparison of the various design choices has not yet been reported in the literature. This article presents a systematic comparison of design choices for SNN-based equalizers and demappers in intensity modulation with direct detection systems, evaluating their impact on bit error rate, spike activity, and model size. The results reveal that design and encoding choices affect these metrics differently, leading to inherent trade-offs.

I. INTRODUCTION

Dense ANN computation can make communication receivers power-hungry, while SNNs use time-dependent neurons that communicate through event-based spikes. Although prior SNN equalizers and demappers show promise, their differing design choices and channel conditions have not been systematically compared; this paper evaluates those choices across BER, spike activity, and model size.

I. INTRODUCTION

  • Dense matrix multiplications make ANN-based receivers computationally complex and often power-hungry, motivating interest in sparse, event-driven SNN computation.SNNs communicate through discrete spikes, and the cited work describes their energy use as potentially a fraction of comparable ANNs.Source: §I · p. 1
  • A systematic comparison is missing because prior approaches vary in decision feedback, hidden-layer recurrence, neural encoding, regularization, and channel conditions.These differences make direct comparison difficult.Source: §I · p. 2
  • The comparison evaluates decision feedback, recurrent connections, two neural encodings, and regularization across 16 SNN equalizer-demapper designs per link, using BER, spikes per inference, and model parameters.It also analyzes how encoding parameters affect performance.Source: §I · p. 2

A. Spiking Neurons

  • Spiking neurons have internal states and represent information through time-dependent binary events called spikes.The LIF example describes incoming spikes charging membrane potential until it crosses a threshold, producing an output spike and reset.Source: A. Spiking Neurons · p. 2

B. The Leaky-Integrate-and-fire Neuron Model

The LIF model represents spiking-neuron dynamics through a membrane potential and synaptic current that evolve over time. Interconnected spiking neurons form layered SNNs, which may include recurrent connections and are trained here with BPTT and surrogate gradients.

B. The Leaky-Integrate-and-fire Neuron Model

  • The LIF neuron integrates incoming spikes into synaptic current and membrane potential while both decay; crossing the firing threshold emits a spike and resets the membrane voltage.The decay rates are set by τs and τm, respectively.Source: B. The Leaky-Integrate-and-fire Neuron… · p. 2
  • Forward Euler integration discretizes the LIF differential equations at fixed time steps, yielding discrete-time neuron dynamics.The time step ∆t is the system sampling time.Source: B. The Leaky-Integrate-and-fire Neuron… · p. 2

C. Spiking Neural Networks

  • An SNN connects spiking neurons through adaptable weights in input, hidden, and output layers; recurrent connections can excite or inhibit neurons.The paper trains SNN weights with backpropagation through time and surrogate gradients, propagating error across layers and simulation steps.Source: C. Spiking Neural Networks · pp. 2–3

D. Neural Encoding

Neural encoding converts real-valued inputs into spike sequences for SNN processing. The section presents receptive-field and quantization encodings, which represent inputs through spike timing or through which signals fire.

D. Neural Encoding

  • Both encoding methods distribute real-valued input information across Nenc spike signals, but RFE uses spike timing while QE uses the first-step firing subset.The figures illustrate an RFE pattern for y = 0.33 and QE patterns for y = 0.33 and y = 0.66.Source: D. Neural Encoding · p. 3, 1) Linear Receptive Field Encoding · pp. 3–4, 2) Quantization Encoding · p. 4
  • Receptive-field encoding (RFE) maps an input to one spike per encoding signal, with distinct inputs represented by spike timing and firing order.For linear RFE, field centers and widths determine timing; the paper discretizes those times for the SNN.Source: 1) Linear Receptive Field Encoding · p. 3
  • Quantization encoding (QE) quantizes an input, maps the result to a binary sequence, and uses the subset of signals firing at the first time step to encode it.The quantizer range is controlled by ymax.Source: 2) Quantization Encoding · p. 4

E. Neural Decoding

Neural decoding converts SNN activity into an output representation. For classification, the paper describes end-of-time membrane-potential decoding to select an estimated class label.

E. Neural Decoding

  • End-of-time membrane-potential decoding estimates a class label by comparing output-neuron membrane potentials at the end of the simulation.The number of output neurons equals the number of classes.Source: E. Neural Decoding · p. 4

III. SNN-BASED EQUALIZATION AND DEMAPPING

The section distinguishes no-feedback and decision-feedback SNN equalizers and demappers, then describes how the NF-SNN encodes recent received samples and decodes a symbol-class estimate.

III. SNN-BASED EQUALIZATION AND DEMAPPING

  • NF-SNN omits feedback of recent symbol estimates, whereas DF-SNN incorporates those estimates,.The paper considers both structures for SNN-based equalization and demapping.Source: §III · p. 4

A. NF-SNN Equalizer and Demapper

  • The NF-SNN encodes the most recent received samples into spike matrices, runs the SNN for K time steps, and decodes a symbol-class estimate before bit demapping.After each decision, neuron states are reset and communication time advances.Source: A. NF-SNN Equalizer and Demapper · p. 4
  • For the non-coherent systems considered, the transmit-symbol set is assumed to be real-valued, X ⊂ R.Source: A. NF-SNN Equalizer and Demapper · p. 4
  • Table I presents the number of trainable parameters for different architectures.Source: Table I · p. 5

B. DF-SNN Equalizer and Demapper

The DF-SNN adds a decision-feedback path that returns recent symbol estimates to the network. The section also describes how architecture determines parameter counts and how training regularization targets spike activity.

B. DF-SNN Equalizer and Demapper

  • The DF-SNN feeds recent received samples and recent symbol estimates through separate paths; EOTM decoding produces the estimate passed to the bit demapper and feedback path.A one-hot encoder converts the estimate into a feedback spike signal with a single spike indicating its class label.Source: B. DF-SNN Equalizer and Demapper · p. 5

C. Number of Model Parameters

  • Input-neuron counts depend on architecture: NF-SNN uses ntapNenc, while DF-SNN uses nffNenc + nfb|X|; both use |X| output neurons.The paper uses a single hidden layer, optionally with recurrent connections, to compute trainable-parameter counts.Source: C. Number of Model Parameters · p. 5

D. Spike Activity Regularization

  • The regularization loss combines squared-weight terms with a penalty for deviation from a target number of hidden-layer spikes, and is added to the task loss during training.The weight terms concern input-to-hidden and hidden-to-output connections; the activity term uses hidden-neuron spikes over samples and time steps.Source: D. Spike Activity Regularization · p. 5

IV. RESULTS

The study evaluates 16 SNN equalizer and demapper implementations across two simulated IM/DD link settings. It compares BER, hidden-layer spike activity, and model size, and benchmarks the best-performing SNNs against FIR and ANN receivers.

A. Implemented Architectures

B. Applied Channels

  • The evaluation uses low- and high-chromatic-dispersion short-reach IM/DD links, focusing on a regime dominated by optoelectronic nonlinearities, including square-law photodetection.The channel model includes chromatic dispersion and direct detection; attenuation is neglected because the model focuses on dispersion and nonlinear effects.Source: B. Applied Channels · p. 6, Table II · p. 6

C. Comparison Metrics

  • BER measures equalizer and demapper performance, Savg measures hidden-layer spike activity as a proxy for energy per symbol decision, and Nθ indicates model size and associated memory or hardware requirements.Source: C. Comparison Metrics · p. 6
  • The best-performing SNN is compared with FIR-based MMSE and decision-feedback receivers and structurally matched ANN receivers, including a DF-ANN supplied with QE.The FIR benchmarks use Lloyd-Max hard-decision detection, and the benchmark equalizers use the same number of taps as their SNN counterparts.Source: C. Comparison Metrics · p. 6

D. Hyperparameters

The section gives training and encoding settings, then reports sensitivity analyses of encoding parameters, regularization, and results across independent runs.

D. Hyperparameters

  • Training uses a fixed noise power of σ2 n = −20 dB, batch size Bt = 5 · 10^4, and 10^5 epochs with Adam at learning rate 10^-3.The SNNs use BPTT with SG for optimization, and evaluation uses 10^7 samples.Source: D. Hyperparameters · p. 7

E. Sensitivity and Robustness Analysis

  • For the NF-SNN on the LCD link, without regularization or recurrent connections, RFE BER remains unchanged down to K = 6 while Savg decreases from ≈90 at K = 60 to ≈30 at K = 6.The passage also reports that QE’s BER and Savg are independent of K and fixes K = 6 for both encodings in subsequent simulations.Source: Figure 8 · p. 7, 1) Influence of Neural Encoding… · p. 8
  • For both encodings, BER deteriorates and Savg decreases when Nenc < 8, with greater BER deterioration for RFE; subsequent comparisons use Nenc = 8.The comparison is shown in Fig. 8(b).Source: Figure 8 · p. 7, 1) Influence of Neural Encoding… · p. 8
  • For RFE with Nenc = 8, regularization has negligible apparent BER effect while significantly reducing Savg for K > 4.The authors characterize regularization as reducing hidden-layer spike activity while maintaining low BER; Fig. 9 compares the regularized and unregularized cases.Source: 2) Impact of Regularization · p. 8, Figure 9 · p. 8
  • Across ten independent initializations, the reported BER and Savg intervals for the displayed architectures are very small at σ2 n = −20 dB.The boxplots summarize ten separately optimized runs; Fig. 10 shows their distributions.Source: 3) Statistical Significance Across Runs · p. 8, Figure 10 · p. 8

F. Results: LCD link

For the LCD link, the SNN implementations have similar BER, while their spike activity and model size differ. Against benchmark receivers, they achieve smaller BER; the best-BER and lowest-activity/size designs differ.

F. Results: LCD link

  • For σ2_n = −20 dB, the 16 implementations achieve similar BER; QE generally has lower BER than RFE, and regularization reduces Savg with negligible BER effect.Recurrence yields minor BER improvements but increases Savg without regularization; NF-SNNQE,R,rec has the lowest BER among the implementations.Source: F. Results: LCD link · p. 8
  • Across the considered σ2 n range, all three SNN-based equalizers and demappers outperform benchmark receivers without neural encoding; at BER 10^-3, NF-SNNQE,R,rec gains approximately 0.7 dB over DF-ANN.Source: F. Results: LCD link · p. 9
  • For Nenc = 8, decision feedback uses 480 fewer parameters than no feedback, while recurrence adds 1,600 parameters; DF-SNNQE,R has the lowest Nθ and Savg.The parameter comparison is shown in Table IV; a non-recurrent DF-SNN is preferred for low-complexity implementations.Source: F. Results: LCD link · pp. 8–9, Table IV · p. 9
  • NF-SNNQE,R,rec has the best BER, whereas DF-SNNQE,R minimizes Savg and Nθ at a minor BER cost.The SNN approaches have similar BER overall but differ substantially in spike activity and model size.Source: F. Results: LCD link · p. 9

G. Results: HCD Link

For the HCD link, decision feedback and recurrence improve BER, and the best BER/activity design is DF-SNNQE,R,rec. The comparisons also show that temporal processing, not input encoding alone, accounts for SNN performance in this setting.

G. Results: HCD Link

  • At BER 10^-3, DF-SNNQE,R,rec gains approximately 1 dB over DF-ANN and achieves the best BER, outperforming the other equalizers.Omitting decision feedback degrades performance; DF-SNNRFE,R, using 68.75% of DF-SNNQE,R,rec's parameters, performs similarly to NF-SNNQE,R,rec.Source: Figure 14 · p. 10, G. Results: HCD Link · p. 10
  • For σ2_n = −20 dB, DF-SNN implementations generally outperform NF-SNNs; some DF-SNNs reach BER below 2 · 10^-4, while no NF-SNN reaches below 4 · 10^-4.Recurrence lowers BER for all approaches, regularization reduces Savg, and the best BER and Savg are achieved by DF-SNNQE,R,rec; encoding shows no clear BER trend.Source: G. Results: HCD Link · p. 10, Figure 13 · p. 10
  • For Nenc = 8, decision-feedback architectures have fewer parameters than NF-SNNs, and recurrence increases Nθ; DF-SNNRFE,R is best among non-recurrent DF-SNNs.NF-SNNQE,R,rec is the best-performing NF-SNN; parameter counts are presented in Table V.Source: G. Results: HCD Link · p. 10, Table V · p. 10
  • RNN equalizers with QE outperform ANN counterparts and perform similarly to SNN counterparts on the HCD link.This comparison supports the paper's interpretation that temporal processing, rather than neural encoding alone, underlies SNN performance in this setting.Source: G. Results: HCD Link · p. 11, Figure 15 · p. 11

H. Discussion

Across both investigated links, SNN equalizers and demappers outperform benchmark receivers in BER, while architectural and encoding choices create trade-offs among BER, spike activity, model size, and latency. The discussion also identifies hardware implementation and full-pipeline energy measurement as future work.

H. Discussion

  • SNN equalizers and demappers outperform benchmark receivers in BER on both links; decision feedback is especially beneficial under severe ISI.The high-dispersion link is harder to equalize, while scaling SNN model complexity allows low BER to be maintained.Source: H. Discussion · p. 11
  • Decision feedback improves high-dispersion ISI mitigation; recurrent connections lower BER but increase model size and spike activity, while activity regularization suppresses spiking without changing model size.Regularization maintains low BER when the loss remains dominated by cross-entropy.Source: H. Discussion · p. 11, Table VI · p. 11
  • At K = 6 and Nenc = 8, QE and RFE perform comparably; below K = 6, RFE degrades significantly while QE remains approximately stable.For low K and thus low latency, QE is the preferred encoding scheme.Source: H. Discussion · p. 11
  • The designs offer trade-offs across BER, average spikes per inference, model size, and latency, so the equalizer and demapper should be adapted to application requirements.Relevant goals include low BER, low spike activity, a small model, or low latency.Source: H. Discussion · p. 11
  • Future work will implement the receiver end to end on custom neuromorphic hardware and realize QE encoding directly in the analog domain to avoid digital-conversion overhead.The proposed QE realization uses cascaded continuous-time comparators that evaluate halved thresholds and emit asynchronous spikes.Source: H. Discussion · p. 11
  • Exact energy-per-bit savings for the complete receiver, including front-end encoding, remain unquantified pending physical ICs integrating analog encoding frontends and neuromorphic spiking cores.The passage identifies this as an ongoing research effort.Source: H. Discussion · p. 12

V. CONCLUSION

The paper systematically compares SNN-based equalizers and demappers for IM/DD systems affected by chromatic dispersion and nonlinear distortion. It finds that design choices trade off BER, spike activity, model size, and latency, with the preferred design depending on application goals.

V. CONCLUSION

  • The study compares decision feedback, recurrent connections, neural encodings, regularization, and encoding parameters for SNN-based IM/DD equalizers and demappers.The systems considered are affected by chromatic dispersion and nonlinear distortion.Source: §V · p. 12
  • Recurrent connections can improve BER while increasing model size and spike activity; training-time regularization reduces spikes while approximately maintaining BER.For links with more severe chromatic-dispersion-induced ISI, decision feedback can significantly improve BER.Source: §V · p. 12
  • SNN equalizers and demappers outperform traditional approaches in the reported comparisons, with design choices offering trade-offs suited to application-specific goals.Those goals include low BER, fewer spikes per inference, low latency, or reduced model complexity.Source: §V · p. 12
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