A Comparative Study of Polar Code Constructions for the AWGN Channel
A Comparative Study of Polar Code Constructions for the AWGN Channel
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发表时间：
2015-01
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通讯作者：
Harish Vangala;E. Viterbo;Yi Hong
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作者：
Harish Vangala;E. Viterbo;Yi Hong
我们提出了一个比较研究的各种极化码结构的性能在加性白色高斯噪声（AWGN）信道。极化码构造是在误码率（BER）方面的设计信噪比（design-SNR）下在$N$个可能的极化比特信道中选择$K$个最佳的任何算法。最佳极化码构造是困难的，因此已经以不同的计算复杂度提出了许多次佳极化码构造。极化码也是非通用的，这意味着码随着设计SNR而显著变化。然而，不知道哪种构造算法在什么设计SNR下构造最佳极化码。我们首先全面调查了所有著名的极化码构造沿着及其完整实现。然后，我们提出了一种启发式算法，以找到最佳的设计信噪比，从给定的构造算法构造最好的极化码。所提出的算法涉及几个可能的设计SNR之间的搜索。最后，我们使用我们的算法进行比较，不同的建设算法，使用广泛的模拟。我们发现，所有的极化码构造算法生成同样好的极化码在AWGN信道中，如果设计SNR优化。
We present a comparative study of the performance of various polar code constructions in an additive white Gaussian noise (AWGN) channel. A polar code construction is any algorithm that selects $K$ best among $N$ possible polar bit-channels at the design signal-to-noise-ratio (design-SNR) in terms of bit error rate (BER). Optimal polar code construction is hard and therefore many suboptimal polar code constructions have been proposed at different computational complexities. Polar codes are also non-universal meaning the code changes significantly with the design-SNR. However, it is not known which construction algorithm at what design-SNR constructs the best polar codes. We first present a comprehensive survey of all the well-known polar code constructions along with their full implementations. We then propose a heuristic algorithm to find the best design-SNR for constructing best possible polar codes from a given construction algorithm. The proposed algorithm involves a search among several possible design-SNRs. We finally use our algorithm to perform a comparison of different construction algorithms using extensive simulations. We find that all polar code construction algorithms generate equally good polar codes in an AWGN channel, if the design-SNR is optimized.