A New Polar Code Design Based on Reciprocal Channel Approximation
A New Polar Code Design Based on Reciprocal Channel Approximation
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DOI：
10.1109/tcomm.2022.3227280
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发表时间：
2022-04
影响因子：
8.3
通讯作者：
H. Ochiai;Kosuke Ikeya;P. Mitran
中科院分区：
文献类型：
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作者：
H. Ochiai;Kosuke Ikeya;P. Mitran
本文重新探讨了当接收器采用逐次消除（SC）解码时，二元输入加性白高斯噪声（BI-AWGN）信道的极性编码设计。我们将重点放在所谓的倒易信道近似（RCA）上，在设计低密度奇偶校验（LDPC）码时经常采用这种方法。RCA 的实现需要计算 BPSK 信令的互信息以及被称为倒易信道映射的相应函数，因此我们开发了这些函数的严格闭式近似值，不仅易于数值计算，而且在宽信噪比范围内有效。通过数值评估，我们发现，与基于流行的高斯近似（GA）和所谓的改进 GA（IGA）的方法相比，所提出的 RCA 方法能更好地估计极化信道的误码率，而且不增加计算成本。因此，采用所提出的 RCA 方法设计的极化编码可以进一步提高块误码率（BLER）性能。随着码字长度的增加，新方法所实现的增益也变得非常显著。
This paper revisits polar code design for a binary-input additive white Gaussian noise (BI-AWGN) channel when successive cancellation (SC) decoding is applied at the receiver. We focus on the so-called reciprocal channel approximation (RCA), which is often adopted in the design of low-density parity-check (LDPC) codes. Implementation of RCA requires the computation of the mutual information of BPSK signaling as well as a corresponding function known as the reciprocal channel mapping, and thus we develop rigorous closed-form approximations of these that are easy to calculate numerically and also valid over a wide range of SNR. Through numerical evaluation we find that, compared to approaches based on the popular Gaussian approximation (GA) as well as the so-called improved GA (IGA), the proposed RCA approach offers better estimates of the bit error rate of polarized channels with no additional computational cost. As a result, polar codes designed by the proposed RCA can achieve further improvement in terms of block error rate (BLER) performance. The gain achieved by the new approach becomes significant as the codeword length increases.