We propose a multi-tap look-up-table(LUT)-based error-tracking decision feedback equalizer with partial unrolling(ET-DFEPU) algorithm to improve log-likelihood ratio(LLR) quality with error propagation. We introduce an error-tracking model to obtain the probabilities of different error states, which are input into the decoder to obtain more accurate LLRs. We also use LUTs to reduce the computation complexity of ET-DFE-PU. Moreover, we adopt a low-complexity partially unrolled architecture to relax the feedback timing constraint. We conduct experiments to transmit 170-Gb/s 4-ary pulse amplitude modulation signal in intensity modulation and direct-detection system at C-band. The results show that the proposed method can achieve 3-d B receiver sensitivity improvement at the same post-forward error correction bit error ratio compared with the conventional DFE.