# Modified Joint Source-Channel Trellises for Transmitting JPEG Images over Wireless Networks
## 4 Simulated Results
Figure 7 illustrates the average PSNR of the reconstructed image versus the SNR over an AWGN channel for different bandwidth compression ratio values. Each case in Figure 7 was generated by expurgating random block codes for a specific channel SNR and then evaluating the performance of the system parameters on the JPEG image for varying SNR values. Each test case demonstrates the performance of our proposed two-tiered JSCC model under different channel conditions. The results of these tests (1) reveal the performance of our method under channel conditions that differ from those for which the conventional tandem system is most suited and (2) illustrate the robustness of the proposed JSCC to variations in channel quality. Moreover, the tested channel conditions were inferior to the encoding conditions optimized for the BCJR algorithm. Performance under these conditions indicates that our JSCC model is more robust to channel quality and exhibits superior resistance to performance degradation in the channel environment. Figure 8 depicts the observed gradual improvement in the quality of the reconstructed images before performance peaked as expurgations exceeded a threshold value. Figure 8 displays the results of applying our two-tiered JSCC method over a channel with AWGN. In the Lena image tested, the maximum VLC length in the joint VLC/linear block code structure was 33. The BPP (Bits Per Pixel) was approximately 0.42 bits/pixel, encoded in shortened random block codes. We tested different SNRs ranging from 2 to 25 over an AWGN channel. Figure 8 reveals that the SNR of the model's modified BCJR algorithm over such a channel was approximately 4 dB larger than the SNR of the conventional tandem system (SNR = 25 dB). We tested different SNRs ranging from 2 to 25; the SNR for our JSCC system was approximately 4-5 dB larger than the SNR of the conventional tandem system, with a BPP of \(\approx\)0.42 bits/pixel. Our JSCC model demonstrated superior BER and  
Figure 6: Normalized delay power spectrum recommended by the IEEE for the 802.11b channel mode. PSNR performance over a wireless channel. By using the proposed JSCC system, BER decreased rapidly as the PSNR increased. However, the results demonstrated excellent image robustness in the case of the AWGN channel. Next, we evaluated the performance of our JSCC model over a slow-fading Rayleigh channel with AWGN, using the channel impulse response randomly sampled from the complex Gaussian distribution for each test image. The system does not consider the time-selective channel. Moreover, the sample frequency and the root mean square delay spread denote \(f_{\mathrm{s}}=3\times 10^{6}(T_{\mathrm{s}}=1/f_{\mathrm{s}})\) and \(\tau_{rms}=10^{-7}\) to \(10^{-6}\), respectively. In the slow-fading channel, the channel gain was randomly sampled from the complex Gaussian distribution for each transmitted image. Channel gain remained constant during the transmission of the entire image. In Figure 9, we plot the performance of the proposed JSCC algorithm over a slow-fading Rayleigh channel as a function of the bandwidth compression ratio for different expurgations of a random code. Our JSCC algorithm allowed us to calculate performance for any bandwidth compression ratio of JPEG images at the average SNR value. As in our AWGN test case, we assumed that the JPEG image was encoded at a rate equal to the capacity of the complex AWGN channel at the average SNR value. When the channel capacity exceeded the transmission rate, the transmitted codewords were decoded reliably through expurgation, and we observed that our JSCC model outperformed the conventional tandem model at all SNR and bandwidth compression ratio values. By using the expurgating strategy, PSNR decreased as the robustness increased. The results demonstrated reliable robustness when PSNR \(>\) 23 dB. In the experiments, the simulated results were obtained in a special wireless scenario where the channel model utilized an 802.11b channel mode subject to slow or frequency fading.