Encoding and Decoding of Non-Binary LDPC Codes with MATLAB Implementation

This article presents MATLAB implementations for encoding and decoding non-binary LDPC codes. Non-binary LDPC codes represent an advanced coding technique in communication systems, offering superior error correction capability and higher data transmission rates compared to their binary counterparts. The encoding/decoding process involves reconstructing original data from received codewords through sophisticated algorithms. The MATLAB implementation demonstrates: - Construction of non-binary LDPC parity-check matrices using finite field arithmetic (GF(q) operations) - Efficient encoding algorithms leveraging sparse matrix properties for reduced computational complexity - Belief propagation decoding implementations with: * Q-ary sum-product algorithm (QSPA) for soft-decision decoding * Fast Fourier transform-based message passing for computational efficiency * Log-domain implementations to prevent numerical instability Code optimization techniques include: - Precomputation of lookup tables for finite field operations - Vectorized processing for parallel message updates - Memory-efficient sparse matrix storage formats These implementations provide a foundation for understanding non-binary LDPC code mechanics while allowing customization for specific research requirements or practical applications. The modular code structure enables straightforward modification of code parameters (field size, code rate, iteration counts) and serves as an ideal starting point for both academic research and engineering implementations in communication systems.