Simulation of Error Rate Performance for Digital Fountain Codes with Different Lengths in Gaussian Channels

This research conducts error rate performance simulation of digital fountain codes with different lengths in Gaussian channels. The simulation involves generating fountain codes using LT (Luby Transform) or Raptor code algorithms with varying block sizes, transmitting through AWGN (Additive White Gaussian Noise) channel models with different SNR (Signal-to-Noise Ratio) values. We evaluate the Bit Error Rate (BER) performance by implementing Monte Carlo simulations with iterative decoding processes using belief propagation algorithms. The study analyzes the relationship between code length, decoding success probability, and overhead requirements, examining the application potential of digital fountain codes in communication systems. Through this research, we gain better understanding of digital fountain code behavior in Gaussian channels, providing valuable references for future communication technology development. Key implementation aspects include: Gaussian noise generation using randn function, modulation/demodulation schemes, and iterative decoding threshold optimization.