# Design and Analysis of Joint Source-Channel Code System with Fixed-Length Code
## 5 Results and Discussion  
### Systems Parameters  
In this section, to verify the performance of the proposed JSCC system in both symbol error rate and decoding complexity, we choose four benchmark schemes for comparison: (1) the separate source-channel code (SSCC), (2) the VLC-IrRNSC, (3) the LBC-RSC, and (4) LBC-IrRNSC. Simulation with the Gaussian distribution source [26] is performed. The discrete source symbols obey the occurrence probabilities that resulted from the 16-ary Lloyd-Max quantization of independent Gaussian distributed source. The source entropy is \(H(S)~{}=~{}3.76\) bits/symbol. Table 3 lists the constituent encoders of different systems. For all systems, 16 QAM Gray mapping is used as the modulation scheme, and a random interleaver is used. The number of source symbols per frame is set to 5000. An additive white Gaussian noise (AWGN) channel is assumed for transmission. For a fair comparison between different systems, all systems are designed to have the same overall code rate of about R = 0.66, i.e., 2.64 bits/channel-use for 16 QAM, and the Shannon limit capacity for the efficiency of 2.64 bits/channel-use is about \(E_{b}/N_{0}~{}=~{}3.4\) dB. To satisfy the requirement for overall code rate, the channel code rate and source code rate are accordingly adjusted in each system. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Source Code** & \multicolumn{2}{c}{**Channel Code**} &
\begin{tabular}{c} **SNR for an** \\ **Open Tunnel** \\ \end{tabular} \\ \hline \multirow{2}{*}{\(L~{}=~{}6\)} & Regular RNSC code & (7, 4) & 8.2 dB \\ \cline{2-4}  & Irregular RNSC code & Subcodes (3, 2), (7, 6) & \\ \cline{2-4}  & Optimum weights [0.36, 064] & 7.8 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of channel code matched with L = 6 source code. Figure 5: Exit curve of optimized channel code for the source code with L = 6. The system consisting of the Huffman code and Turbo code is taken as the benchmarks of the separate source-channel code (SSCC) system. The Turbo code is used to protect the Huffman coded bits from the channel error. The Turbo code consists of two recursive systematic convolutional (RSC) codes with generator polynomial \((7,5)_{8}\), and its output bits are punctured to obtain the code rate 2/3. At the receiver, noniterative source-channel decoding is used. Iterative source-channel decoding is used in JSCC systems, i.e., the VLC-IrRNSC scheme, the LBC-RSC scheme, the LBC-IrRNSC, and our scheme. The VLC-IrRNSC scheme employs a VLC as the source code of and an irregular RNSC code as the channel code. In this scheme, the VLC [6] is constructed for a given free distance of \(d_{f}~{}=~{}3\), and the attained codewords have an average length \(\overline{L}~{}=~{}5.92\). The output bits of VLC encoder are passed through an interleaver and forwarded to the irregular RNSC encoder with a rate 33/32. The irregular code is composed of RNSC subcodes \((3,2)_{8}\) and \((6,7)_{8}\) with optimum weights of 0.86 and 0.14. In the linear block code (LBC)-based JSCC schemes [13], the LBCs are generated based on the linear parity check code. The LBC-RSC scheme employs an LBC with codeword length \(L~{}=~{}5\) as the source code and an 8/9 rate RSC code as the channel code. The LBC adds a single parity bit to the 4-bit quantized source symbol, and the optimized RSC code with generator polynomial \((5,7)_{8}\) also introduces additional redundancy for error correction. The LBC-IrRNSC scheme employs an LBC with codeword length \(L~{}=~{}6\) as the source code and an irregular RNSC code as the channel code. The LBCs are generated based on the rate 2/3 linear parity check code in [15]. The subcodes of the irregular encoder used are \((3,2)_{8}\) and \((7,6)_{8}\), and their optimum weights are 0.08 and 0.92. The output bits of the irregular code are randomly punctured such that the channel code rate was increased as a result of 22/21.