Polar Code Encoding and Decoding under AWGN Channel

This documentation discusses the implementation of polar code encoding and decoding under AWGN (Additive White Gaussian Noise) channels. The program incorporates the calculation of Z-parameters (reliability parameters) for AWGN channels, along with channel polarization indexing and sorting mechanisms. Channel polarization is a communication technique that transforms a complex communication channel into two simpler sub-channels, thereby enhancing communication reliability and efficiency. The implementation utilizes recursive Z-parameter calculations through Gaussian approximation methods to determine channel reliability metrics. The code implementation features a systematic approach to channel polarization where the algorithm first computes the Bhattacharyya parameters for each sub-channel, then performs recursive channel splitting operations. The indexing system employs a bit-reversal permutation to map natural order indices to polarized channel order, while the sorting algorithm uses reliability-based criteria to select the most reliable channels for information bits. Key functions in the implementation include: - calculate_z_parameters(): Computes initial Z-values using SNR-dependent formulas - channel_polarization(): Implements the recursive channel transformation process - reliability_sorting(): Ranks channels based on calculated reliability metrics - bit_reversal_permutation(): Handles index mapping between natural and polarized orders By integrating channel polarization technology into the encoding and decoding process, the program significantly improves coding performance and decoding accuracy. This document provides detailed explanations on using Z-parameters for AWGN channel polarization calculations and demonstrates how indexing and sorting techniques optimize the encoding/decoding implementation through structured algorithm design.