Polar codes: Primary concepts and practical decoding algorithms

Polar codes represent an emerging class of error-correcting codes with power to approach the capacity of a discrete memoryless channel. This overview article aims to illustrate its principle, generation and decoding techniques. Unlike the traditional capacity-approaching coding strategy that tries to make codes as random as possible, the polar codes follow a different philosophy, also originated by Shannon, by creating a jointly typical set. Channel polarization, a concept central to polar codes, is intuitively elaborated by a Matthew effect in the digital world, followed by a detailed overview of construction methods for polar encoding. The butterfly structure of polar codes introduces correlation among source bits, justifying the use of the SC algorithm for efficient decoding. The SC decoding technique is investigated from the conceptual and practical viewpoints. State-of-the-art decoding algorithms, such as the BP and some generalized SC decoding, are also explained in a broad framework. Simulation results show that the performance of polar codes concatenated with CRC codes can outperform that of turbo or LDPC codes. Some promising research directions in practical scenarios are also discussed in the end.