Simplification of probability density function using trapezoidal method in impulsive noise

In environments characterized by impulsive noise, the probability density function (pdf) of noise is inaccessible in closed form and can only be obtained through complex numerical computations. This paper introduces a simplified pdf using the trapezoidal method tailored for such noise. To enhance the reliability of these systems, error correction codes such as Low-Density Parity-Check (LDPC) codes are employed. Depending on the decoding algorithm used, these codes utilize the LLR function or the a posteriori probability (APP) function at their input, both of which rely on the pdf of the noise. In our simulations, we demonstrate that LDPC codes using the simplified pdf for LLR calculations with fixed α and γ, specifically with BPSK (Binary Phase Shift Keying) and ASK-4 modulations, can achieve performance in impulsive noise environments comparable to that obtained using the exact pdf.