Comparison of Polar Code Encoding/Decoding and RM Codes

In this article, we provide a comparative analysis of polar code encoding/decoding and Reed-Muller (RM) codes, highlighting their similarities and differences. First, let's examine polar code encoding/decoding. Polar codes are sophisticated encoding and decoding techniques designed to achieve reliable data transmission in wireless communications and data storage systems. The core algorithm operates through a recursive channel polarization process, where information bits are strategically allocated to the most reliable virtual channels using a reliability sequence (typically calculated through Gaussian approximation or density evolution methods). This transformation enhances transmission reliability by progressively converting information bits into more robust codewords. The primary advantage of polar code encoding/decoding lies in its capacity to efficiently correct communication errors through successive cancellation (SC) or more advanced successive cancellation list (SCL) decoding algorithms, delivering superior reliability. Polar codes find extensive applications in 5G communication systems, satellite communications, and optical fiber transmission networks.

Next, we explore RM codes. RM codes represent a class of block coding schemes employed for error correction during data transmission. Unlike polar codes, RM codes utilize distinct encoding and decoding algorithms based on Boolean functions and polynomial representations. The encoding process involves repeating information bits multiple times combined with added parity-check bits through recursive construction methods (RM(r,m) codes are built using Plotkin's |u|u+v| construction). This structure enhances transmission reliability and facilitates easier error detection and correction through majority-logic decoding or recursive algorithms. RM codes have widespread applications across digital communications, storage systems, and audio/video transmission technologies.

In summary, both polar code encoding/decoding and RM codes serve as advanced coding techniques for improving transmission reliability. While they differ in algorithmic approaches and implementation methodologies - with polar codes leveraging channel polarization and RM codes utilizing algebraic structures - both play crucial roles in modern communication systems. Whether deployed in wireless communications, satellite links, or data storage solutions, these coding technologies provide robust and efficient data transmission capabilities essential for contemporary digital infrastructure.