Multi-Layer Progressive Tree-Structured Edge Growth Algorithm for Nested Lifting Design of 5G-NR-Like LDPC Codes

We proposed an algorithm called multi-layer progressive tree-structured edge growth, to design rate-compatible length-scalable raptor-like quasi-cyclic LDPC codes with nested base matrices and nested lifting, like 5G new radio (NR) LDPC codes. The nested lifting design is mainly investigated in this letter. To deal with the complicated dependency of the performance for nested base matrices and lifting sizes simply and effectively, the design of nested lifting is decomposed into the lifting design of each lifting size, which is called a layer. In each layer, the lifting of nested base matrices is designed via progressive tree-structured edge growth algorithm, where tree structure is employed to reserve diversified intermediate results and achieve better trade-off of error floor performance among nested base matrices. The criterion composed of improved cycle classification, minimum distance test and performance evaluation is employed for tree pruning, which could better optimize the error floor performance under acceptable complexity. The effectiveness of the proposed algorithm is demonstrated via construction and simulation.