Parallel Decoder of Polar Codes

Polar codes, a recent discovery in coding theory, represent a groundbreaking family of capacity-achieving codes. They stand out as the first codes to achieve capacity for any binary discrete memoryless channel (B-DMC), constructed through the innovative channel polarization concept. Building upon the advancements in polar code techniques, this paper introduces a high-speed decoder rooted in the successive cancellation (SC) decoding framework. The focus here is on presenting the core concepts and techniques behind channel polarization, polar codes, and the high-speed decoding algorithm, enabling the parallel decoding of N bits simultaneously. The implementation of polar codes over binary erasure channels (BEC) is demonstrated, and their bit error rates are calculated at varying erasure probabilities. Through simulation results, we showcase the performance of polar codes when subjected to high-speed decoding.