The core idea of Polar code is to "polarize" a set of independent and identically distributed channels into a set of new virtual channels through a specific transformation. Some of these virtual channels will have very good channel characteristics (close to noiseless), while others will have very poor channel characteristics (close to pure noise). Through this polarization effect, those good channels can be selected to transmit information bits, while the poor channels can be used to transmit fixed redundant bits (such as zero bits), thereby achieving efficient coding.

Channel polarization: Polar codes use channel polarization technology to identify channels with high channel capacity among a large number of virtual channels for transmitting information.

Scalability: The length of Polar codes is a power of 2, which makes them easily expandable according to different application requirements.

Low complexity decoding: Polar codes can be decoded using an algorithm called Success Probability Decoding (SCD), which has low complexity.

Close to the Shannon limit: Under block length and high signal-to-noise ratio, Polar codes can approach the channel capacity, that is, the Shannon limit.

Disadvantages of Polar Codes

Although Polar codes have many advantages in theory, they still face some challenges in practical applications, such as:

Limited block length: In practical systems, due to the limitations of decoding complexity and delay, very long codewords cannot be used, which may affect the ability of Polar codes to approach the Shannon limit.

Channel estimation: The performance of Polar codes is highly dependent on accurate knowledge of channel state information (CSI), so accurate channel estimation is required.

Decoding algorithm: Although the SCD algorithm has low complexity, in order to further improve performance, more complex decoding algorithms such as list decoding are usually required.

In a summary, Polar codes have a good balance between performance and complexity and are more advantageous in the case of medium and short code lengths. In short, polarization coding theory can have a broad application prospect in practical communication systems, and there are a large number of application problems worth studying, such as source coding, multi-user communication, physical layer confidential communication, etc. Some of these problems have attracted the attention of some scholars, but even for these problems, most of the research on them is still only in the theoretical stage. In order to be actually deployed and applied in future communication systems, a lot of research work is still needed.