Low-complexity soft decision detection for combating DFE burst errors in IM/DD links

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The deployment of non-binary pulse amplitude modulation (PAM) and soft decision (SD)-forward error correction (FEC) in future intensity-modulation (IM)/direct-detection (DD) links is inevitable. However, high-speed IM/DD links suffer from inter-symbol interference (ISI) due to bandwidth-limited hardware. Traditional approaches to mitigate the effects of ISI are filters and trellis-based algorithms targeting symbol-wise maximum a posteriori (MAP) detection. The former approach includes decision-feedback equalizer (DFE), and the latter includes Max-Log-MAP (MLM) and soft-output Viterbi algorithm (SOVA). Although DFE is easy to implement, it introduces error propagation (EP). Such burst errors distort the log-likelihood ratios (LLRs) required by SD-FEC, causing performance degradation. On the other hand, MLM and SOVA provide near-optimum performance, but their complexity is very high for high-order PAM. In this paper, we consider a one-tap partial response channel model, which is relevant for high-speed IM/DD links. We propose to combine DFE with either MLM or SOVA in a low-complexity architecture. The key idea is to allow MLM or SOVA to detect only $3$ typical DFE symbol errors, and use the detected error information to generate LLRs in a modified demapper. The proposed structure enables a tradeoff between complexity and performance: (i) the complexity of MLM or SOVA is reduced and (ii) the decoding penalty due to EP is mitigated. Compared to SOVA detection, the proposed scheme can achieve a significant complexity reduction of up to $94\%$ for PAM-$8$ transmission. Simulation and experimental results show that the resulting SNR loss is roughly $0.3\sim0.4$ dB for PAM-$4$, and becomes marginal $0.18$ dB for PAM-$8$.

Original languageEnglish
Article number10286055
Pages (from-to)1395-1408
Number of pages14
JournalJournal of Lightwave Technology
Issue number5
Early online date16 Oct 2023
Publication statusPublished - 1 Mar 2024


The work of Alex Alvarado was supported by the European Research Council (ERC) through the European Union s Horizon 2020 Research and Innovation Programme under Grant Agreement 757791. This work was supported by the Netherlands Organisation for Scientific Research through the VIDI Grant ICONIC under Grant 15685

FundersFunder number
European Union's Horizon 2020 - Research and Innovation Framework Programme757791
European Research Council
Nederlandse Organisatie voor Wetenschappelijk Onderzoek15685


    • fiber chan
    • fiber nonlinearities
    • pulse amplitude modulation
    • decision- feedback equalizer
    • Decision feedback equalizers
    • Complexity theory
    • soft-output Viterbi algorithm
    • MAP algorithm
    • Direct detection
    • Viterbi algorithm
    • Precoding
    • Symbols
    • Forward error correction
    • intensity modulation
    • soft-decision decoding
    • Detection algorithms
    • decision-feedback equalizer


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