edVirtus Reference

What Are Polar Codes?

What Are Polar Error-Correcting Codes?

Polar Codes are a family of forward error correction (FEC) codes that can achieve communication rates approaching the theoretical maximum predicted by Claude Shannon's Channel Coding Theorem. Introduced in 2009 by the Turkish engineer Erdal Arıkan, Polar Codes are the first class of error-correcting codes proven mathematically to achieve the capacity of a wide range of communication channels. They have become particularly important through their adoption in 5G New Radio (NR) cellular systems.

Like other error-control codes, Polar Codes improve communication reliability by adding carefully designed redundancy to the transmitted information. The receiver uses this redundancy to detect and correct transmission errors caused by noise, interference, and fading. Their distinguishing feature is a process known as channel polarization, which transforms a set of identical communication channels into a new set of virtual channels that become either highly reliable or highly unreliable.

The encoder places information bits only into the highly reliable virtual channels, while the unreliable channels are assigned predetermined values known as frozen bits. Because the receiver already knows the values of the frozen bits, it can use this additional information during decoding to recover the original message with a very low probability of error.

A useful analogy is a group of roads connecting two cities. Suppose some roads are consistently smooth and reliable, while others are rough and frequently blocked. Rather than sending traffic equally over every road, a planner routes important vehicles along the reliable roads and reserves the poor roads for maintenance vehicles. Polar Codes apply the same principle mathematically by sending information only through the most reliable virtual channels.

The most widely used decoding method is Successive Cancellation (SC) decoding, in which the receiver estimates each information bit one at a time, using previous decisions to improve subsequent ones. Although computationally efficient, SC decoding may be less effective for short code lengths. Practical systems therefore often employ Successive Cancellation List (SCL) decoding, frequently combined with a Cyclic Redundancy Check (CRC), to achieve significantly improved error-correction performance.

One of the principal advantages of Polar Codes is their excellent performance for short and moderate block lengths, together with relatively low implementation complexity. These characteristics made them particularly attractive for the control channels of 5G New Radio (NR), where reliable communication with relatively short messages is essential.

It is important to distinguish Polar Codes from Low-Density Parity-Check (LDPC) Codes. Both operate close to the Shannon limit, but they employ fundamentally different mathematical principles. LDPC codes use sparse parity-check matrices and iterative decoding, whereas Polar Codes rely on channel polarization and successive decoding. In the 5G standard, Polar Codes are used primarily for control-channel coding, while LDPC codes are used for high-speed user-data channels, allowing each coding technique to be applied where its strengths are greatest.

Today, Polar Codes are regarded as one of the most significant advances in modern coding theory. Their mathematical proof of capacity achievement, together with their adoption in 5G mobile communications, has established them as one of the major error-control coding techniques alongside BCH, Reed–Solomon, Turbo, and LDPC codes. They represent an important milestone in the continuing effort to approach the fundamental limits of reliable digital communication.