# Area-Efficient Early-Termination Technique for Belief-Propagation Polar Decoders
## 4 Experimental Results  
To compare various early-termination criteria, we simulated (1024, 512) polar decoding under different channel conditions. For a fair comparison, we carefully set the maximum decoding iteration \(T\) at 40 and the threshold value at 3.5, obtained from a previous study [15], to maintain the same level of error-correcting performance. Thus, the early-termination criteria [15; 16; 17] did not affect the error-correcting performance but affected the average number of decoding iterations. Figure 7 shows the average number of decoding iterations for the conventional [8], threshold-based [15], information-BER-based [16], frozen-BER-based [17], and proposed methods. In the conventional BP decoder with no early-termination technique, 40 decoding iterations were required regardless of the SNRs. The previous threshold-based [15] and proposed early-termination methods [15; 16; 17] have the same number of decoding iterations, as the proposed method simplifies circuitry checking without  
Figure 6: Proposed early-termination structure for (8, 4) polar codes. affecting the decoding performance. The information-BER-based [16] and the frozen-BER-based [17] methods require a slightly higher number of decoding iterations compared with the threshold-based [15] and proposed methods. For a complexity comparison, termination check circuitries for different methods were implemented using 65-nm CMOS (complementary metal-oxide-semiconductor) technology with an operating frequency of 200 MHz. All the internal LLR values are assumed as 4 bits. Figure 8 shows the equivalent gate counts for polar (1024, \(K\)) according to the code rate \(R=K/N\). As the code rate increases, the equivalent gate count of the information-BER-based [16] and proposed methods increases, and frozen-BER-based [17] method decreases gradually. For code rate up to 0.6, the proposed algorithm requires the smallest equivalent gate counts, and the frozen-BER-based [17] method has the smallest count when the code rate is higher. Figure 9, gate counts according for polar (\(N\), \(N/2\)) to the code length with the code rate = 1/2. According to Figure 8, as for (1024, 512) polar codes, the proposed method can reduce hardware complexities by 72.7%, 66.5%, and 59.7% compared to the previous threshold-based [15], information-BER-based [16], and frozen-BER-based [17] methods, respectively. Figure 7: Average number of iterations for different early-termination methods. To sum up, Table 1 summarizes the additional hardware resources required to check the termination condition for different early-termination methods. For previous information-BER-based [16] and frozen-BER-based [17] methods, the single-bit or double-bit operators including adders and XORs are not taken into account so as to simplify the complexity comparison. The previous threshold-based method [15] requires circuitry checks associated with both information and frozen bit channels; previous windowing methods, including information-BER-based [16] and frozen-BER-based [17] methods, require circuitry checks associated with either entire information bit channels or frozen bit channels. Whereas the windowing methods [16; 17] inevitably demand registers to save intermediate values, the proposed method simplifies the threshold-based method [15] based on Propositions 1 and 2, resulting in the smallest hardware complexity without any registers. Furthermore, many applications using polar codes adopt a polar code with a small code rate. For instance, 5G communication recently  
Figure 8: Equivalent gate counts of threshold-based [15], information-BER-based [16], frozen-BER-based [17], and proposed early-termination algorithms according to code rate. Figure 9: Equivalent gate counts of threshold-based [15], information-BER-based [16], frozen-BER-based [17], and proposed early-termination algorithms according to code length. adopted polar codes as control channel error correction codes, and the 5G control channel uses a small polar code with a code rate (\(K\)/\(N\)) less than 1/2.