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Article summary:

1. Belief propagation list (BPL) decoding of polar codes has been proposed for achieving state-of-the-art performance.

2. A two-step approach is proposed for the joint design of permutations and polar code under BPL decoding, including an empirical approach for selection of good initial permutations and a joint optimization of permutations and polar code based on genetic algorithm.

3. With the aid of an outer cyclic redundancy check (CRC) code, the proposed BPL scheme is shown to perform very close to CRC aided successive cancellation list (CA-SCL) decoding at practical SNRs.

Article analysis:

The article provides a comprehensive overview of the joint design of permutations and polar codes under BPL decoding, with a two-step approach that includes an empirical approach for selection of good initial permutations and a joint optimization of permutations and polar code based on genetic algorithm. The article also provides evidence that the proposed BPL scheme performs very close to CRC aided successive cancellation list (CA-SCL) decoding at practical SNRs when aided by an outer cyclic redundancy check (CRC) code.

The article appears to be reliable in its claims, as it provides evidence from experiments conducted to support its conclusions. Furthermore, the authors provide detailed explanations regarding their methods and approaches used in their research, which adds credibility to their findings.

However, there are some potential biases in the article that should be noted. For example, the authors focus mainly on BP-tailored codes constructed via bit swapping or by a genetic algorithm, while SC-tailored codes are not discussed in detail or compared against BP-tailored codes in terms of performance. Additionally, there is no discussion about possible risks associated with using BPL decoding or any other potential drawbacks that could arise from using this method.

In conclusion, this article appears to be reliable overall but should be read with caution due to potential biases present in its content.