# Averting BER Floor with Iterative Source and Channel Decoding for Layered Steered Space-Time Codes
## 4 Simulation Results and EXIT Analysis
As all the inner LSSTC curves in Figure 2 are intersecting the outer curve prior to the (1, 1) point, it is plausible that the LSSTC-SP-URC-\(\text{SBC}^{*}_{[2,6]}\) scheme is ineffective in achieving infinitesimal BER. However, the inner LSSTC curves and the outer curve of the combined SISO module for the optimized LSSTC-SP-URC-\(\text{SBC}_{[2,6]}\) arrangement succeed in attaining the (1, 1) point of perfect convergence as shown in Figure 3. As discussed above, the Kliewer criterion is met for the convergence of LSSTC-SP-URC-\(\text{SBC}_{[2,6]}\) scheme. More specifically, the open EXIT tunnel between the curves provides the effective basis for attaining infinitesimal BER. Moreover, the Monte-Carlo based trajectories for the \(E_{b}/N_{0}\) values of 8 to 13 dB are recorded by the exchange of MI between the inner SP demapper  
Figure 3: Outer and inner EXIT curves for the LSSTC-SP-URC-\(\text{SBC}_{[2,6]}\) scheme along with Monte-Carlo based decoding trajectories at \(E_{b}/N_{0}=8\) to 13 dB. Figure 2: Outer and inner EXIT curves for the LSSTC-SP-URC-\(\text{SBC}^{*}_{[2,6]}\) scheme along with Monte-Carlo based decoding trajectories at \(E_{b}/N_{0}=8\) to 13 dB. module. The Monte-Carlo simulation also confirms our claim that the LSSTC-SP-URC-SBC\({}_{[2,6]}\) scheme is more favourable than the LSSTC-SP-URC-SBC\({}_{[2,6]}^{*}\) because it attains the goal of maximum extrinsic value of \(I_{E}(outer)=1\) even at an \(E_{b}/N_{0}\) of 1 dB, whereas the LSSTC-SP-URC-SBC\({}_{[2,6]}^{*}\) scheme is unable to attain the said goal at any value of \(E_{b}/N_{0}\), as shown in the trajectories of Figure 2.  
The BER performance curves of the schemes presented in Table 2 are shown in Figure 4. The schemes in Table 2 are making use of the persistent overall code rate, but they differ only in the values of \(d_{H,\min}\). It is clearly seen in Figure 4 that the BER curve associated with LSSTC-SP-URC-SBC\({}_{[5,15]}\) requires the least \(E_{b}/N_{0}\) to reach the \(10^{-4}\) BER value. Consequently, the BER performance of LSSTC-SP-URC-SBC\({}_{[5,15]}\) scheme is the best among others owing to the \(d_{H,\min}\) value of 6, providing infinitesimal BER. The URC assists in attaining lower BER by distributing the information across the decoders and higher \(d_{H,\min}\) values result in better distribution. Thus, the BER floor is not seen for higher than \(10^{-4}\) values for the optimized SBC schemes. It is worthy to mention that the inner and outer iterations of the three-stage LSSTC system with ISCD become beneficial in acquiring the reliable LLR values. In other words, the information after the inner and outer iterations is refined enough to be more accurately fed to the SBC decoder for an enhanced BER. Moreover, the LSSTC-SP-URC-SBC\({}_{[2,6]}^{*}\) benchmarker offers the least BER performance as the \(d_{H,\min}=1\) is unable to offer any iterative gain for EXIT convergence. More specifically, an \(E_{b}/N_{0}\) gain of about 15 dB exists at the BER value of \(10^{-4}\) for the LSSTC-SP-URC-SBC\({}_{[5,15]}\) scheme in comparison to the benchmarker. Figure 5 depicts the PSNR performance trends of the schemes presented in Table 2. The PSNR performance curves also advocate for the LSSTC-SP-URC-SBC\({}_{[5,15]}\) scheme across the entire \(E_{b}/N_{0}\) range. It is visible from Figure 5 that the LSSTC-SP-URC-SBC\({}_{[5,15]}\) outperforms the benchmarker by about 22 dB at the PSNR degradation point of 41 dB. The reason for the high gain in the PSNR is that we have employed a very compression efficient H.265 video codec, with the capability to reduce huge raw format video stream into considerably less amount of data. However, it is very important to note that the impact of transmission errors on the performance of decoded video stream becomes extremely gross on highly compressed video stream.