Finite-Length Puncturing Pattern Design for LDPC Codes With Hadamard Constraints

In this letter, we propose a two-stage method to design finite-length puncturing patterns for LDPC codes with Hadamard constraints. At the first stage, we propose the distribution of puncturing patterns and develop extrinsic information transfer functions for distribution optimization in terms of the lowest decoding threshold. At the second stage, we analyze the iterative update process of a Hadamard check node (HCN) and find that the Euclidean distance determines the reliability of its output extrinsic information. Based on this, we propose a greedy algorithm to design puncturing patterns to maximize the number of punctured variable nodes with reliable input information. Simulations verify the good performance of the Hadamard-LDPC code with our designed puncturing patterns, compared to the 5G new radio LDPC code and the same Hadamard-LDPC code with other puncturing patterns.