## 5 Simulation Results and Discussion
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Turbo Equalization with 5 it.** & **BER (Range)** \\ \hline Figure 9a & h1 = [0.18 0.85 0.32] & \(10^{-3}\) \\ Figure 9b & h2 = [0.302 0.725 0.456] & \(10^{-2}\)–\(10^{-3}\) \\ Figure 9c & h3 = [0.407 0.815 0.407] & \(10^{-2}\)–\(10^{-3}\) \\ \hline \multicolumn{3}{c}{**Separate MMSE equalization and LDPC decoding with 40 it.**} \\ \hline
**Graphic** & **h** & **BER (range)** \\ \hline Figure 10a & h1 = [0.18 0.85 0.32] & \(10^{-5}\)–\(10^{-6}\) \\ Figure 11a & h2 = [0.302 0.725 0.456] & \(10^{0}\)–\(10^{-1}\) \\ Figure 12a & h3 = [0.407 0.815 0.407] & \(10^{0}\)–\(10^{-1}\) \\ \hline \multicolumn{3}{c}{**Separate MMSE equalization and LDPC decoding with 80 it.**} \\ \hline
**Graphic** & **h** & **BER (range)** \\ \hline Figure 10b & h1 = [0.18 0.85 0.32] & \(10^{-5}\)–\(10^{-6}\) \\ Figure 11b & h2 = [0.302 0.725 0.456] & \(10^{0}\)–\(10^{-1}\) \\ Figure 12b & h3 = [0.407 0.815 0.407] & \(10^{0}\)–\(10^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: BER vs. SNR in an ISI channel, at the SNR of 5 dB, using turbo equalization and the equalization performed separately before the decoding process applying MMSE equalizer and LDPC decoding for different impulse responses h.  
Figure 12: BER vs. SNR, using separately MMSE equalization and LDPC decoder, h3 = [0.407 0.815 0.407]; (a) LDPC decoder makes 40 it and (b) LDPC decoder makes 80 it. Table 4 summarizes the BER vs. SNR performances of the proposed system, turbo equalization, and separate MMSE equalization with LDPC decoding. It can be noticed that the proposed system's results for h1 are comparable to separate equalization with MMSE and better than turbo equalization, as can be deduced from Tables 1 and 2. On the other hand, MMSE with LDPC yields poor results, ranging from \(10^{0}\) to \(10^{-1}\) for h2 and h3. The system model proposed in this study (LDPC decoder performs 20 iterations) outperforms turbo equalization for an SNR higher than 4 dB for the channel with h1. For a channel with h2 and h3, for an SNR higher than 7 dB, the system proposed by us (when LDPC decoder performs 20 iterations) is more efficient than turbo equalization and MMSE with LDPC decoding. If we deviate from the standard and do not puncture the first 2\(Zc\) bits and transmit 440 bits in the case of the proposed system, for the three h, the results are presented as follows in Figure 13a-c. The coding rate is approximately \(\%\), not being adjusted by puncturing. We considered the situation in which the LDPC decoder performs 20 iterations during one iteration of the iterative process of equalization and decoding. Table 5 highlights the performances of the system proposed in this study (the LDPC decoder makes 20 iterations at one iteration of the iterative equalization and decoding process) with puncturing and without puncturing the first 2\(Zc\) bits, for the SNR of 5 dB. The results are better than in the case of puncturing the first 2\(Zc\) bits according to standard. The equalizers and decoders do not always match equally well to each other to obtain satisfactory results. But in this paper, it was found a combination between the Log-MAP equalizer and the min-sum LDPC decoder that offers the presented performances. In addition, it was made a comparison of the proposed scheme with other established models in the specialized literature, such as turbo equalization or MMSE equalization combined with LDPC decoding.