# DLSTM-Based Successive Cancellation Flipping Decoder for Short Polar Codes
## 4 Performance Analysis
### BER and BLER Analysis  
In Figure 16 left, we compare the error-correction performance for the proposed algorithm with \(T_{1}=4\), \(T_{2}=2\), \(4\), and \(T_{3}=4\) for \(P(32,16)\). The proposed decoder adopts a 4-bit CRC and its generator polynomial is \(g(x)=x^{4}+x+1\). It can be noticed that, with continuous flipping, a lot of gain can be achieved. When \(\text{BLER}=10^{-3}\), the proposed algorithm with \(T_{1}=4\), \(T_{2}=2\), and \(T_{1}=4\), \(T_{2}=4\) can achieve gains of approximately 0.32 dB and 0.57 dB than that with \(T_{1}=4\), respectively. At \(\text{BER}=10^{-4}\), the proposed algorithm with \(T_{1}=4\), \(T_{2}=2\), and \(T_{1}=4\), \(T_{2}=4\) can obtain performance improvement of about 0.25 and 0.46 dB compared to that with \(T_{1}=4\), respectively. The error-correction performance of the proposed algorithm with \(T_{1}=4\) and \(T_{2}=4\) is close to that with \(T_{1}=4\), \(T_{2}=4\), and \(T_{3}=4\). This is due to the occurrence of three errors with low frequency. In Figure 16 right, the block length is changed to 64. The proposed algorithm with \(T_{1}=4\) and \(T_{2}=4\) is lower than that with \(T_{1}=4\), \(T_{2}=2\), and \(T_{1}=4\) in terms of the BLER and the BER. The proposed algorithm for \(N=32\) has a significant performance gain compared to that for \(N=64\). On the one hand, the shorter is the block length, the higher is the prediction accuracy. On the other hand, the degree of channel polarization for \(N=64\) is better than for \(N=32\). A polar code with \(N=64\) has fewer error bits than that with \(N=32\). Figure 14: Comparison of average normalized decoding complexity for \(P(64,32)\) with \(T_{1}=4\), \(T_{2}=2\). Figure 15: (**left**) Comparison of total decoding latency for \(P(32,16)\). (**right**) Comparison of total decoding latency for \(P(64,32)\). Figure 17 left shows the BLER performance of the proposed algorithm compared with the existing algorithms for \(P(32,16)\) with \(T_{\max}=6\). It can be seen that the proposed algorithm significantly outperforms the ML-MSCF decoder and the DSCF decoder within the same number of flips. It is also more efficient than CA-SCL (\(L=2\), \(L=4\)). It is close to the performance of CA-SCL (\(L=8\)). As shown in Table 4, the proposed algorithm can achieve approximately 0.28 and 0.49 dB performance gain, but the decoding latency is increased by 5.77% and 1.16% over the ML-MSCF decoder and the DSCF decoder at BLER = \(10^{-3}\). Compared with CA-SCL (\(L=2\), \(L=4\)), it can obtain performance gain of about 0.66 and 0.19 dB, and the decoding latency is reduced by 15.73% and 31.22%, respectively. The performance is slightly lower than that of CA-SCL (\(L=8\)), but the decoding latency is decreased by 51.46%. In Figure 17 right, compared with the ML-MSCF decoder, DSCF decoder, and CA-SCL (\(L=2\), \(L=4\)), the proposed algorithm has lower BER. Figure 16: (**left**) Performance comparison of different flip times for \(P(32,16)\). (**right**) Performance comparison of different flip times for \(P(64,32)\). Figure 17: (**left**) BLER comparison of different algorithms for \(P(32,16)\). (**right**) BER comparison of different algorithms for \(P(32,16)\). Figure 18 compares the BLER performance for \(P\)(64, 32) with \(T_{\text{max}}=6\). It can be noticed that the proposed algorithm has better error-correction performance than the ML-MSCF decoder, DSCF decoder, and CA-SCL (\(L\) = 2). It is close to the performance of CA-SCL (\(L\) = 4). Table 5 shows the obtained gains and reduced latency using the proposed algorithm over other algorithms at BLER = \(10^{-3}\). The proposed algorithm achieves a gain of about 0.21 dB compared to the ML-MSCF decoder, but the decoding latency is slightly increased. Compared with the DSCF decoder and the CA-SCL (\(L\) = 2) decoder, the proposed algorithm can obtain gains of about 0.36 and 0.55 dB, and decoding latency is reduced by 1.39% and 19.29%, respectively. The performance is slightly lower than that of CA-SCL (\(L\) = 4), but the decoding latency is decreased by 45.41%. This is due