This paper studies the diversity of protographbased quasi-cyclic low-density parity-check (QC-LDPC) codes over nonergodic block-fading channels under iterative beliefpropagation decoding. We introduce diversity evolution (DivE), a Boolean-function-based analysis method that tracks how the fading dependence of belief-propagation messages evolves across decoding iterations. Under a Boolean approximation of block fading, DivE derives a Boolean fading function for each variable node (VN) output (i.e., the a-posteriori reliability after iterative decoding), from which the VN diversity order can be directly determined. Building on this insight, we develop a greedy blockmapping search that assigns protograph VNs to fading blocks so that all information VNs achieve full diversity, while including the minimum additional parity VNs when full diversity is infeasible at the nominal rate. Numerical results on the 5G New Radio LDPC codes show that the proposed search finds block mappings that guarantee full diversity for all information bits without modifying the base-graph structure, yielding a markedly steeper high-SNR slope and lower BLER than random mappings.

翻译：本文研究了基于原图的准循环低密度奇偶校验码在非遍历块衰落信道下、采用迭代置信传播解码时的分集性能。我们提出了分集演化方法，这是一种基于布尔函数的分析方法，用于追踪置信传播消息的衰落依赖性在解码迭代过程中的演变。在块衰落的布尔近似下，分集演化方法为每个变量节点输出（即迭代解码后的后验可靠性）推导出一个布尔衰落函数，从而可以直接确定变量节点的分集阶数。基于这一见解，我们开发了一种贪婪的块映射搜索算法，该算法将原图变量节点分配到衰落块中，使得所有信息变量节点均实现满分集；在标称码率下无法实现满分集时，则纳入最少数量的额外校验变量节点。在5G新空口LDPC码上的数值结果表明，所提出的搜索算法能够在不改变基图结构的前提下，找到保证所有信息位均获得满分集的块映射方案，相较于随机映射，该方案呈现出显著更陡的高信噪比斜率及更低的误块率。