## 5 Simulation Results and Discussion  
The simulation results were attained using Matlab and are presented in the following. As a rule, all graphics were plotted for an SNR that varies between 0-10 dB, but where the graphics display values for SNR lower than 10 dB, it means that in those cases, no more errors were found over the respective values. In the iterative process of equalization and decoding, there are iterations carried out in both the ensemble process (equalization-decoding) and within the LDPC decoder. It should be mentioned that in this work, five iterations were performed within the iterative process of equalization and decoding. During one iteration of the iterative receiver, the LDPC decoder performs either 10 or 20 iterations, depending on the specific situation being analyzed. This process is illustrated in Figure 5.  
We arranged all the simulation scenarios in Table 1 to make it easier for the reader to follow. \begin{table}
\begin{tabular}{c c c} \hline
**A. Analyzing the Contribution of the Log-MAP Equalizer of the Proposed System in Terms of BER vs. SNR, Considering** \\
**h1 = [0.18 0.85 0.32]** \\ \hline \hline
**Graphic/Scenario** & **Iterative Receiver** & **Min-Sum LDPC Decoder** \\ \hline \hline
**Figure** 6a/1 st Scenario** & 2 iterations (it0 and it1) & 10 iterations at each iteration it0 and it1 \\ \hline \hline
**Figure** 6a/2 nd Scenario** & 1 iteration (test) & 20 iterations \\ \hline \hline
**Figure** 6b/1 st Scenario** & 2 iterations (it0 and it1) & 20 iterations at each iteration it0 and it1 \\ \hline \hline
**Figure** 6b/2 nd Scenario & 1 iteration (test) & 40 iterations \\ \hline \hline
**B. Analyzing the performances in terms of BER vs. SNR of the proposed system, considering different h’s** \\ \hline \hline
**Graphic** & **Iterative Receiver** & **Min-Sum LDPC Decoder** & **h** \\ \hline \hline
**Figure** 7a & 5 iterations & 10 iterations & h1 = [0.18 0.85 0.32] \\ \hline \hline
**Figure** 7b & 5 iterations & 10 iterations & h2 = [0.302 0.725 0.456] \\ \hline \hline
**Figure** 7c & 5 iterations & 10 iterations & h3 = [0.407 0.815 0.407] \\ \hline \hline
**Figure** 8a & 5 iterations & 20 iterations & h1 = [0.18 0.85 0.32] \\ \hline \hline
**Figure** 8b & 5 iterations & 20 iterations & h2 = [0.302 0.725 0.456] \\ \hline \hline
**Figure** 8c & 5 iterations & 20 iterations & h3 = [0.407 0.815 0.407] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of all simulation scenarios. Figure 5: The iterative receiver proposed for ISI channels. To notice the role of the Log-MAP equalizer, two scenarios were considered. In the first scenario, iteration 0 (it0) and iteration 1 (it1) were considered in the iterative process of equalization and decoding. In iteration 0 (it0), the Log-MAP equalizer does not receive any a priori information from the min-sum LDPC decoder, thus realizing the a posteriori information only based on the data observed from the channel output [5]. At each of the two iterations of the iterative receiver, the LDPC decoder makes ten iterations. In the second scenario, there is only one iteration (test) in the iterative process of equalization and decoding. The number of iterations in the decoder is 20, which is the sum of the cumulative iterations of the first scenario (10 by 10). In it0, the a posteriori information from the equalizer is deinterlaced and then provided to the decoder. In the case of iteration 0 (it0) the Log-MAP equalizer does not receive any a priori information from the decoder. On the other hand, iteration 1 (it1) involves the whole iterative process of equalization and decoding. The a posteriori information from the equalizer is deinterlaced and then provided to the decoder. The Log-MAP equalizer receives the a priori information from the decoder after it has been interlaced. So, the second scenario (test) is like it0, only that the decoder makes more iterations. The analysis was conducted by considering h1 = [0.18 0.85 0.32].