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Article summary:

1. 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.

2. The proposed reciprocal channel approximation (RCA) approach offers better estimates of the bit error rate of polarized channels with no additional computational cost.

3. Through numerical evaluation, it is found that polar codes designed by the proposed RCA can achieve further improvement in terms of block error rate (BLER) performance, especially as the codeword length increases.

Article analysis:

The article provides a comprehensive overview of the design of polar codes over a binary-input additive white Gaussian noise (BI-AWGN) channel, focusing on the so-called reciprocal channel approximation (RCA). The authors provide rigorous closed-form approximations to calculate numerically and valid over a wide range of SNR, which are easy to calculate and offer better estimates of the bit error rate than other approaches such as Gaussian Approximation (GA) or Improved GA (IGA).

The article is generally reliable and trustworthy, providing detailed information about the design process and its advantages over other approaches. The authors provide evidence for their claims through numerical evaluation and simulation results, which demonstrate that RCA-based designs can offer better bit error rate (BER) as well as block error rate (BLER) estimates compared to GA-based approaches. Furthermore, they provide rigorous closed-form expressions to approximate the mutual information for BPSK signaling as well as its inverse, which can be used to design polar codes with long codeword lengths.

However, there are some potential biases in the article that should be noted. For example, while the authors discuss various techniques proposed for polar code design over a BI-AWGN channel such as density evolution or learning based approaches like genetic algorithms or reinforcement learning, they do not explore these methods in detail or compare them to RCA in terms of performance gains. Additionally, while they mention that RCA was initially proposed in [22] and [23], they do not discuss these works in depth or compare their findings with those presented here. Finally, while they note that their approach supports a wide range of SNR after polarization, they do not provide any evidence for this claim or discuss how this affects performance gains achieved by their approach compared to other methods.