Effect study of the probability of error on the frozen bit positions in polar codes

Polar codes are a channel coding technique designed to achieve the symmetric capacity of a binary input discrete memoryless channel (BI-DMC). Constructing polar codes involves selecting the most reliable channels from a set of polar sub-channels, which are linear combinations of the original channel outputs . This paper examines the relationship between error probability and the positions of frozen bits in polar codes, considering different channel models, including the Binary Erasure Channel (BEC), Binary Symmetric Channel (BSC), and Additive White Gaussian Noise (AWGN) channel, while maintaining a constant code length. The study aims to understand how variations in error probability affect the reliability of sub-channels. These variations, in turn, influence the position of the frozen bits, which play a crucial role in the encoding process. By exploring these factors, the research seeks to optimize polar codes for different communication scenarios, enhancing performance by gaining a deeper understanding of how error probabilities and frozen bit positions interact across various channel conditions.