Performance analysis of polar codes based on 3 × 3 kernel matrix

In this paper, polar codes are constructed based on 3 ? 3 kernel matrix G3 rather than the classic 2 ? 2 kernel matrix G2 proposed by Arikan. Since the distance spectrum is a powerful tool to estimate the maximum likelihood performance of block codes, it can be applied to analyze the performance tendency of the above mentioned polar codes. Both the union bound and simulation results show that systematic polar codes (SPCs) have better performance of bit error rate (BER) than the non-systematic polar codes (NSPCs) while they have the same frame error rate (FER) performance. Meanwhile, the performance comparison relied on distance spectrum between polar codes with G2 kernel matrix and those with G3 kernel matrix shows that the former has better performance.