MATLAB Implementation of LDPC Encoding and Decoding Based on GF(q)

This is a MATLAB-based LDPC (Low-Density Parity-Check) encoding and decoding program implementing GF(q) finite field operations. The program enables complete LDPC encoding and decoding processes through MATLAB function implementations. During encoding, the program performs computations based on GF(q) finite field arithmetic principles, generating corresponding encoded outputs using matrix multiplication operations between generator matrices and input data vectors. The decoding module utilizes GF(q) decoding algorithms, specifically implementing belief propagation or iterative decoding methods to recover original data from noisy channel outputs. Key functions include GF(q) arithmetic operations (addition, multiplication, inversion), parity-check matrix initialization, and iterative message-passing decoding routines. Written entirely in MATLAB language, the program features straightforward function calls and can be easily integrated and executed within the MATLAB environment for both simulation and practical communication system implementations.