# Design and Analysis of Joint Source-Channel Code System with Fixed-Length Code
## 5 Results and Discussion
### Convergence and SER Performance  
We use EXIT curves for analyzing the convergence performance of the schemes in Table 3. In Figure 6a-c, the well-matched EXIT curves of the outer SBSD and the irregular channel decoder are illustrated. The decoding trajectories are also acquired by recording the mutual information at the input and output of decoders during the Monte Carlo simulation. It can be seen that, at the bit SNR \(E_{b}/N_{0}\) of 4.2 dB, an open EXIT tunnel is obtained and the decoding trajectory can reach the (1,1) point in the proposed scheme. This indicates that the convergence threshold of iterative decoding is 4.2 dB. Similarly, open EXIT tunnels are obtained at 4.6 dB for both the LBC-IrRNSC scheme and the VLC-IrRNSC scheme. With \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Source Code**} & \multirow{2}{*}{**Irregular RNSC Channel Code**} & **Bit SNR for an** \\  & & & **Open Tunnel** \\ \hline Variable – length code \(d_{f}~{}=~{}3\) &
\begin{tabular}{c} Subcodes (3, 2), (6, 7) \\ optimum weights [0.86, 0.14] \\ Subcodes (3, 2), (7, 6) \\ optimum weights [0.80, 0.92] \\ Subcodes (3, 2), (7, 6) \\ optimum weights [0.36, 064] \\ \end{tabular} & 4.6 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of irregular RNSC code matched with different source code. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Scheme**} & \multirow{2}{*}{**Source Code**} & \multirow{2}{*}{**Source Code**} & **Channel Code** & **Channel** & **Overall Rate** \\  & & & **Code Rate** & **Code Rate** & **Code Rate** \\ \hline SSCC & Huffman & 0.99 & Rate-3/5 Turbo code & 2/3 & 0.66 \\ VLC-IrRNSC & Variable – length code \(d_{f}~{}=~{}3\) & 0.64 & Irregular RNSC code & 33/32 & 0.66 \\ LBC-RSC & Linear block code \(L~{}=~{}5\) & 0.75 & RSC code & 8/9 & 0.66 \\ LBC-IrRNSC & Linear block code \(L~{}=~{}6\) & 0.63 & Irregular RNSC code & 22/21 & 0.66 \\ Proposed \(L~{}=~{}6\) & optimized block code \(L~{}=~{}6\) & 0.63 & Irregular RNSC code & 22/21 & 0.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of different source channel coding schemes. the aid of an EXIT chart, the convergence threshold of each scheme is obtained, and we list them in Table 5 for comparison. It can be concluded that the SSCC scheme has the worst converge performance, and our scheme with L = 6 achieves the best converge performance compared to the other JSCC schemes. Figure 6: The EXIT chart of the different JSCC schemes using Irregular RNSC codes. (**a**) The EXIT chart of the VLC-IrRNSC scheme. (**b**) The EXIT chart of the LBC-IrRNSC scheme with L = 6. (**c**) The EXIT chart of the proposed scheme with L = 6. The SER performance of all the schemes is illustrated in Figure 7. It can be seen that the proposed scheme achieves the best performance compared to benchmark schemes. The proposed scheme obtains the waterfall region at about \(E_{b}/N_{0}~{}=~{}4.2\) dB, which is within a 1 dB deviation from the Shannon limit. The simulation results are also verified in the EXIT chart predictions. Compared to the SSCC scheme, the proposed scheme obtains about a 1 dB gain at the SER of \(10^{-4}\). The parameters of source and channel encoders are jointly optimized in our scheme. Therefore, the residual redundancy in the source-coded bits is efficiently exploited by ISCD, resulting in SNR gains. In comparison with the VLC-IrRNSC scheme, our scheme has a 0.5 dB gain. The performance improvement can be attributed to the inherent synchronization of the fixed-length codes and the well-matched IrRNSC code. The VLC codes suffer from error propagation in source symbol decisions when some errors remain after iterative decoding, while our fixed-length block code avoids the problem. Additionally, the fixed-length codes also have a low decoding complexity. Compared with the LBC-RSC scheme and LBC-IrRNSC scheme, our scheme also obtains a gain of 0.3 dB and 0.8 dB at the SER of \(10^{-4}\).