## 4 Experimental Results  
In this section, an analysis of the achievable system rates and the BER results are presented to illustrate the advantage of the proposed codes. Figures 4-7 plot the achievable system rates for the proposed codes with different source probabilities. For instance, in Figure 6, the achievable system rates \(R=C_{W}/H(p)\) versus \(E_{s}/N_{0}\) with four typical source probabilities \(p\) (0.9, 0.92, 0.94, 0.96) for the proposed code \(B_{s}^{1/2}\) are provided. In addition, the curves for \(B_{s}^{0.94}\), which is proposed for \(p=0.94\) in [17], are also provided for comparison. Note that \(p=0.9\) (\(H(p)=0.469\)) is the smallest probability that satisfies the lossless source coding theorem (\(H(p)\leq R_{s}\)) for \(R_{s}=0.5\) when \(\delta=0.02\). It can be found that \(B_{s}^{1/2}\) and \(B_{s}^{0.94}\) have similar shaping gaps to the Shannon limits for \(p=0.94\) and \(p=0.96\) at the target system rate \(R=6\). However, as the source probability decreases, the proposed \(B_{s}^{1/2}\) can achieve an advantage over \(B_{s}^{0.94}\). Specifically, for \(p=0.9\), the JSCCM system with the proposed \(B_{s}^{1/2}\) can obtain a 0.19 dB shaping gain over \(B_{s}^{0.94}\), reducing the gap to the Shannon limit. Thus, for the whole considered range of source probabilities, the proposed source code can obtain a better PAS performance than \(B_{s}^{0.94}\). Furthermore, in Figures 4-7, observe that in a range of source probabilities, the gaps to the Shannon limits for the proposed codes are all within 0.6 dB at the target system rates, which can ensure the PAS performance for varying source probabilities. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Source Codes** & \(W\) & **Source Decoding Threshold** &
\begin{tabular}{c} **Gap** \\ \(\mathbf{R_{s}-H^{th}}\) \\ \end{tabular} \\ \hline \(\mathbf{B}_{s}^{3/4}\) & \((3,3,5)\) & \(p^{th}=0.812\), \(H^{th}=0.6973\) & 0.0527 \\ \(\mathbf{B}_{s}^{3/5}\) & \((5,5,5)\) & \(p^{th}=0.877\), \(H^{th}=0.5379\) & 0.0621 \\ \(\mathbf{B}_{s}^{1/2}\) & \((7,7,7)\) & \(p^{th}=0.912\), \(H^{th}=0.4298\) & 0.0702 \\ \(\mathbf{B}_{s}^{1/3}\) & \((11,11,13)\) & \(p^{th}=0.951\), \(H^{th}=0.2821\) & 0.0512 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Source decoding thresholds for the proposed source codes. Figure 4: Achievable system rates for the proposed source code \(B_{s}^{3/4}\) (target system rate \(R=4\)). Figure 5: Achievable system rates for the proposed source code \(B_{s}^{3/5}\) (target system rate \(R=5\)). Figure 6: Achievable system rates for different source codes (\(R_{s}=1/2\), target system rate \(R=6\)). To further verify the merits of the proposed source codes, we present some bit-error-rate (BER) results of JSCCM systems with 16 ASK for different source probabilities. For all simulations, an AWGN channel was assumed, and the information block length was fixed at 3600 bits. Additionally, the maximum number of iterations was set to 100. For source codes with different coding rates, the same protograph LDPC code (3/4-rate-\(\mathbf{B}_{c}^{LU}\)[23]) was employed as the channel code. The existing source code with a good PAS performance for JSCCM systems (1/2-rate-\(\mathbf{B}_{s}^{0.94}\)[17]), the code with a good source decoding threshold (1/3-rate-\(\mathbf{B}_{s}^{LFloor}\)[19]), and 3/5-rate regular LDPC were utilized as benchmark codes. The base matrices for these benchmark codes are provided as follows:  
\[\mathbf{B}_{s}^{0.94}=\left( \begin{array}{ccccccccc}1&1&3&3&1&0\\ 1&0&5&2&0&1\\ 1&2&3&3&1&1\end{array} \right). \tag{22}\]  
\[\mathbf{B}_{s}^{LFloor}=\left( \begin{array}{ccccccccccccc}3&2&1&1&0&1&0&0&2 &0&2&0\\ 2&3&1&0&1&0&1&0&3&2&0&0\\ 3&3&0&0&0&0&0&1&3&0&0&1\\ 3&0&1&2&2&1&1&1&2&2&1&2\end{array} \right). \tag{23}\]  
\[\mathbf{B}_{s}^{regular}=\left( \begin{array}{ccccccccc}2&1&1&1&0\\ 1&0&1&2&1\\ 0&2&1&0&2\end{array} \right). \tag{24}\]  
The BER curves of JSCCM systems with the proposed source codes for different source probabilities are depicted in Figures 3 and 8-10.