  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. 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 error propagation 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 to 0.4 dB
for PAM-4, and becomes marginal 0.18 dB for PAM-8.
