# Improvement of Fast Simplified Successive-Cancellation Decoder for Polar Codes
## 4 Simulation Results  
In this section, we demonstrate the performance of the proposed method with binary phase shift keying (BPSK) over the additive white Gaussian noise (AWGN) channel. The Tal-Vardy algorithm [15] was used to find information set \(\mathcal{A}\) (optimized at SNR = 0 dB for \(N\) = 256, and SNR = 2 dB for \(N\) = 1024, 2048, and 4096). The system polar encoding was implemented according to [16]. The identification of constituent codes on the decoding tree was performed offline. To calculate the ratio of the latency reduction, it was necessary to count the number of codes for each of the constituent code types. The decoding latency was the joint influence on these constituent codes, and the R-other node was the main cause of the latency. Table 1 lists the number of different nodes when \(N=1024\). It was found that, as the code rate increased, the number of R-1 and SPC nodes of longer lengths increased, while the number of R-0 and Rep nodes of longer lengths decreased. \(C(N,R)\) was defined as the average percentage of R-other nodes satisfying the FC for a code of a certain length and rate. Figure 4 shows the average percentage of R-other nodes under the Fast-ISSC decoder for polar codes (256, 1/2), (1024, 3/4), (2048, 1/4), and (4096, 1/2) that satisfy the FC, along with the corresponding SNR. It is shown that the FC of the Fast-ISSC decoder remained valid, the proportion of R-other nodes that satisfied the FC increased with the SNR, and 30% of the R-other nodes satisfied the FC when the SNR was 3 dB. When the SNR was 4.5 dB, 40% of the R-other nodes of the polar codes (1024, 3/4) and (256, 1/2) satisfied the FC. The average ratios of latency reduction compared to the SSC decoder for Fast-SSC, IMSC, and Fast-ISSC for polar codes (1024, 1/4), (1024, 1/2), and (1024, 3/4) with \(P=256\) are compared in Figure 5. Here, \(L(N,R)\) denotes the latency reduction of the Fast-ISSC decoder relative to the SSC decoder for a code of block length \(N\) and rate \(R\), i.e., \(L(N,R)=\frac{\left({{L_{SSC}}(N,R)-{L_{Fast-ISSC}}(N,R)}\right)}{{{L_{SSC}}(N,R)}}\). The \(L(N,R)\) for the Fast-SSC and IMSC decoders are defined in a similar manner. The latencies of both the Fast-ISSC and IMSC are affected by the channel conditions, both of which have the dynamics of the FC method, while the Fast-SSC is independent of the channel condition. The Fast-ISSC achieves the smallest decoding latency compared to the SSC, Fast-SSC, and IMSC decoder, at different code rates and different SNRs. When the SNR is 5 dB, the proposed Fast-ISSC decoder decreases the latency by almost 90% compared to the SSC decoder. In addition, the problem of high latency for the IMSC method at a high code rate and low SNR is solved. To investigate the relationship between the relative gain of the latency and \(P\) PEs, the effects of \(L(4096,1/2)\) using the Fast-ISSC and IMSC for \(P\) varying from 16 to 4096 are shown in Figure 6. The trends of both the Fast-ISSC and IMSC are identical, and the relative gain of the former is greater than that of the latter at each \(P\) value, when the SNR is within the range of 1-2 dB. For SNR \(\geq\) 2.5 dB, the gap between the two methods is gradually reduced. Further, when the value of \(P\) is greater than 256, the improvement in the latency reduction decreases.