Polar code, also known as polar code, is a forward error correction coding (FEC) scheme proposed by Turkish professor Erdal Arıkan in 2008. It is a linear block code considered as a method to achieve channel capacity, especially in the case of high signal-to-noise ratio (SNR). Polar codes have attracted much attention due to their mathematical elegance and extreme performance under certain conditions, and have been selected as one of the control channel coding schemes for 5G communication standards.

Basic principles of polar codes

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

Key Features of Polar Codes

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: Since the length of Polar codes is a power of 2, this makes them easily scalable 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.

Application of Polar Code in 5G

In the 5G communication standard, Polar code is selected as the coding scheme for the control channel, mainly used for the transmission of small packets. Together with another encoding scheme, the LDPC code (Low Density Parity Check Code), it was used to replace the Turbo code used in early communication standards.

Polar codes use recursive transformations to polarize sub-channels into very reliable or very unreliable sub-channels, and then encode only reliable sub-channels.

LDPC codes use a sparse matrix to map message bits to sub-channel bits, and then apply an iterative decoding algorithm to recover the message.

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 real systems, very long codewords cannot be used due to limitations in decoding complexity and latency, 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.

Polar codes have a good balance between performance and complexity, and are more advantageous in the case of short and medium code lengths. In short, polar coding theory can have broad application prospects in actual communication systems, and there are a large number of application issues worthy of study, such as source coding, multi-user communication, physical layer secure communication, etc. Some of these issues have attracted the attention of some scholars, but even for these issues, most of the research on them is still only at the theoretical stage. In order to carry out actual deployment and application in future communication systems, it is still difficult to A lot of research work is required.