# Semantic Communication on Digital Wireless Communication Systems
## 3 IER--A Novel Physical Layer Semantic Metric
### Relation Between IER, BER, and Semantic Metric  
In order to verify the relation between the IER, BER, and semantic communication metric, we designed a test case, as shown below. We chose the bit-conversion JSCC transmission scheme we proposed in Section 2. And the measurement points of the BER, IER, and PSNR at the simulation link are shown in Figure 9.  
In this simulation link, if we keep the bits-to-constellation point mapping unchanged (the mapper and de-mapper module) and employ the 3 GPP 5G bit constellation point mapping scheme [27], then different integer-to-bit conversion coding results cause different integer constellation point mapping results. Obviously, different integer-to-bit conversion coding methods will impact the received data directly. We choose two different integer-to-bit conversion codecs: one is the natural binary coding shown in Figure 10a, and the other is the Manhattan distance binary coding, as shown in Figure 10b, which is designed to make the Manhattan distance of adjacent constellation points smaller. We will introduce more details of this constellation mapping scheme in Section 4. The simulation configuration is illustrated in Table 2. In order to evaluate the relation between the IER, BER, and semantic metric, two identical configurations are employed, except for the different integer-to-bit conversion coding schemes. The transmission framework both used bit-conversion JSCC, which is described in Section 2.1. The quantization output range is [0, 1, 2, 7], which is used to adopt the 64 QAM modulation for the Manhattan distance binary coding. And the channel equalization is LMMSE for both cases, so as to eliminate the impact of different channel types. In a simple way, we choose image as the source file, and then we can compare the simulation results of these two test cases to analyze the relation between the BER, IER, PSNR, and SSIM. And for the semantic codec, the LSCI is chosen for the semantic coding algorithm, which can be used for image and video semantic communication. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Message** & **Integer-Valued** & \begin{tabular}{c} **Manhattan Distance** \\ **Distance to Vector S** \\ \end{tabular} & \begin{tabular}{c} **Natural Binary** \\ **Coding** \\ \end{tabular} & \
\begin{tabular}{c} **Hamming** \\ **Distance to Vector S** \\ \end{tabular} &
\begin{tabular}{c} **BER** \\ **IER** \\ \end{tabular} \\ \hline S & [1, 2, 5, 7] & 0 & [001, 010, 101, 111] & 0 & 0\% & 0\% \\ \hline R1 & [0, 3, 5, 6] & 3 & [000, 011, 101, 110] & 3 & 25\% & 9\% \\ \hline R2 & [5, 2, 1, 3] & 12 & [101, 010, 001, 011] & 3 & 25\% & 37\% \\ \hline R3 & [5, 6, 5, 7] & 8 & [101, 110, 101, 111] & 2 & 16\% & 13\% \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of the BER and IER. Figure 9: Measuring points of metrics in the simulator. The physical layer metrics simulation results are shown in Figure 11. It is observed that, since the physical layer procedure is the same for two test cases, the Hamming distance and BER are almost the same for the two test cases. It can be observed that the BER starts to increase when the SNR is lower than 20 for both cases, which is consistent with the traditional communication performance, since both cases utilized 64 QAM and did not use channel coding.