Efficient Design of MET-LDPC Code Ensembles via Multinomial Parameter Optimization

Designing multi-edge type low-density parity-check (MET-LDPC) code ensembles that satisfy structural constraints while achieving near-capacity performance remains a challenging problem. Existing methods, including those based on differential evolution, have improved flexibility but still face limitations such as high computational cost and the need for manual configuration of edge patterns. We propose an optimization-based method that explores diverse, structurally feasible edge distribution candidates and optimizes node distributions via a constrained linear system formulation. A dual annealing optimizer is then applied to identify node profiles that maximize the decoding threshold. Evaluations on both the binary erasure channel and the binary-input additive white Gaussian noise channel across multiple code rates show that our method consistently produces ensembles with strong threshold performance and low edge complexity, highlighting its practicality and adaptability.