## 6 Conclusions  
In this study, we proposed a system that respects the classic turbo-equalization scheme. We used an LDPC coder for transmission and a Log-MAP equalizer for reception, connected with a min-sum LDPC decoder. We performed the performance analysis of the proposed system, BER vs. SNR, considering three different h functions. It has been experimentally demonstrated that increasing the number of iterations performed by the LDPC decoder from 10 to 20 in the iterative process of equalization and decoding leads to improved results (as can be observed in Table 2, Section 5). Then, the proposed system was compared with turbo equalization and separate equalization with MMSE and LDPC decoding in terms of BER vs. SNR, considering the three different h functions. Based on the analyzed results, the equalization performance depends on both the impulse response of the channel and the chosen decoding and equalization method; some decoding and equalization systems offered better results, depending on h function (as can be observed in Table 4, Section 5). Not puncturing the first 2 Zc bits, the proposed system achieved better BER vs. SNR performance (as can be observed in Table 5, Section 5). In conclusion, Table 6 compares the performances in terms of BER vs. SNR of the proposed approach to others published in the literature, demonstrating its performances. The comparison with other papers in the literature is not the most eloquent because the simulation parameters and the methods differ from those proposed in this paper. In the future, channel estimation, using the least-square (LS) channel estimator, can be integrated into the iterative process of equalization and decoding, and thus BER performance can be improved during iterations. We should also consider performing an EXIT chart analysis as a future perspective. In this paper, we have limited ourselves to LDPC codes and turbo codes, as they are currently considered to be among the most relevant [52; 53]. \begin{table}
\begin{tabular}{l c c} \hline
**BER vs. SNR in an ISI Channel, at the SNR of 5 dB, Comparing the Proposed System to Others Published in the Literature** \\ \hline
**1 st Comparison** & **h** & **BER (Range)** \\ \hline The proposed system-5 it in the iterative process of equalization and decoding, 10 it in the LDPC decoder. & h1 = [0.18 0.85 0.32] & \(10^{-4}\)-\(10^{-5}\)(\(1/8\times 10^{-4}\)) \\ \hline The proposed system-5 it in the iterative process of equalization and decoding, 20 it in the LDPC decoder. & h1 = [0.18 0.85 0.32] & 0 \\ \hline The MAP turbo equalizer implemented in [1] performs 10 iterations. & h = [0.227 0.460 0.688 0.460 0.227] & \(10^{-4}\) \\ \hline
**2 nd comparison** & **h** & **BER (range)** \\ \hline The proposed system-5 it in the iterative process of equalization and decoding, 20 it in the LDPC decoder. & h1 = [0.18 0.85 0.32] & 0 \\ \hline The MAP turbo equalizer implemented in [8] performs 6 iterations. & h = [0.227 0.460 0.688 0.460 0.227] & \(10^{-3}\)–\(10^{-4}\) \\ \hline
**3 rd comparison** & **h** & **BER (range)** \\ \hline The proposed system-5 it in the iterative process of equalization and decoding, 20 it in the LDPC decoder. & h1 = [0.18 0.85 0.32] & 0 \\ \hline The implemented system in [28] designed with cooperative decoding between a BCJR detector and the spatially coupled low-density parity-check decoder performs 5 iterations. & h = [1 1] & \(10^{-4}\)–\(10^{-5}\) (\(1/7\times 10^{-4}\)) \\ \hline \end{tabular}
\end{table} 
Table 6: Comparing the performances in terms of BER vs. SNR of the proposed system to others published in the literature. **Author Contributions:** Conceptualization, A.-M.C., F.L.M. and C.G. ; methodology, A.-M.C. and F.L.M. ; software, A.-M.C. and F.L.M. ; validation, A.-M.C., F.L.M., A.-M.G. and C.G. ; formal analysis, A.-M.G. and C.G. ; investigation, A.-M.C. ; resources, F.L.M. ; data curation, A.-M.C. and A.-M.G. ; writing--original draft preparation, A.-M.C. and F.L.M. ; writing--review and editing, A.-M.C., A.-M.G. and C.G. ; visualization, A.-M.C. and A.-M.G. ; and C.G.