# Hybrid Window Decoding for Joint Source Channel Anytime Coding System
## 4 Simulation and Analysis
The message updates of the JEWD and PJEWD algorithms approximately linearly increase within the observed time slot region. As to the hybrid window decoding of the proposed JHWD algorithm, the adaptive local expanding window decoding strategy with smaller iteration rounds of \(I_{\text{max2}}\) does not result in a significant increase of message updates, which is about 10 times lower than those of the JEWD and PJEWD algorithms at \(t=26\). When the coupling length is \(\gamma=8\), the average message updates of the proposed JHWD algorithm are relatively higher than those of \(\gamma=5\). This experiment indicates that the anytime property of the proposed JHWD algorithm is between the JEWD algorithm and PJEWD algorithm but with lower decoding complexity. Figure 3: Asymptotic decoding complexity analysis based on the density evolution [17; 18]. In Figure 6, the simulation performance of the data chain at the time slot \(t\) = 100 versus \(E_{b}/N_{0}\) is observed. In Figure 6a, the proposed JHWD algorithm has the smallest curve slope in the low signal to noise ratio (SNR) region. In the high SNR region, larger than 1.5 dB, the proposed JHWD algorithm can obtain a lower error floor than that of JEWD algorithm and  
Figure 4: Asymptotic anytime property analysis based on the density evolution [17; 18]. Figure 5: BER performance and decoding complexity of a single message block with \(N^{sc}=64\) bits as the decoding delay within a sliding window region [17; 18]. is closer to the BER performance of the PJEWD algorithm. Figure 6b shows the average message updates normalized by that of the JEWD scheme. The decoding complexity of traditional JEWD does not change with SNR. While the decoding complexities of the proposed JHWD and PJEWD scheme are lower than that of the JEWD scheme, especially in the high SNR region. When \(E_{b}/N_{0}=3\) dB, the average message updates of PJEWD can be decreased about 26.47%, while the proposed JHWD can be decreased about 69.61% compared with the JEWD algorithm. These simulation results show that the proposed JHWD can reduce the decoding complexity to a great extent without sacrificing too much error correction performance. Figure 7 provides the BER performance comparisons with the state of the art, especially the (3,12)- and (3,6)- SC-LDPC-based JSCC scheme with sliding variable-window decoding (SVWD) of comparable window size [16]. As seen in Figure 7, with the same code rates of \(R^{sc}=0.25\), \(R^{cc}=0.5\) and the code length of 6400 bits, the block D-LDPC-based JSCC (LDPC i-8-2-4) [10] has the highest error floor. When the coupling length \(\gamma\) is 3, which is comparable to the syndrome former memory of \(m=2\) in [16] (\(\gamma=m+1\)), and the adaptive decoding window size is \(2\gamma-1=5\) to \(3\gamma-2=7\) (versus the sliding variable-window size of \(W_{f}=3\) to \(W_{max}=6\) in [16]), the SC-RA-based JSCAC with proposed JHWD has a lower error floor. However, as \(\gamma\) is increased to match the larger window sizes of [16], the preponderance of SC-RA-based JSCAC with the proposed JHWD is gradually reduced. When \(\gamma\) is 5, the JSCAC scheme with the proposed JHWD demonstrates a similar performance to the SC-LDPC JSCC scheme with SVWD of \(W_{f}=9\). The narrowing gap might be caused by the mismatch between \(\gamma\) and \(m\) in [16]. Moreover, Figure 7 also shows the BER performance of i.i.d uniform memory-less source with separate channel coding of \(R^{cc}=1/7\) without loss of the transmission rate. Compared with the separate source channel coding system, the JSCC schemes can achieve early error fall regions and better error performances in the low SNR region, but suffer from error floors in the high SNR region. Figure 6: BER performance and decoding complexity of the data chain at the time slot \(t=100\) (L = 100) with \(N^{sc}=64\) bits [17; 18].