This paper investigates the design and performance of delayed bit-interleaved coded modulation (DBICM) with low-density parity-check (LDPC) codes. For Gray labeled square $M$ -ary quadrature amplitude modulation (QAM) constellations, we investigate the optimal delay scheme with the largest spectrum efficiency of DBICM for a fixed maximum number of delayed time slots and a given signal-to-noise ratio. When analyzing the capacity of DBICM, we find two important properties: the capacity improvement due to delayed coded bits being mapped to the real and imaginary parts of the transmitted symbols are independent of each other; a pair of delay schemes with delayed coded bits having identical bit-channel capacity lead to equivalent DBICM capacity. Using these two properties, we efficiently optimize the delay scheme for any uniform Gray-QAM systems. Furthermore, these two properties enable efficient LDPC code designs regarding unequal error protection via bit-channel type classifications. Moreover, we use protograph-based extrinsic information transfer charts to jointly optimize degree distributions and channel assignments of LDPC codes and propose a constrained progressive edge growth like algorithm to jointly construct LDPC codes and bit-interleavers for DBICM, taking distinctive bit-channel’s capacity into account. Simulation results demonstrate that the designed LDPC coded DBICM systems significantly outperform LDPC coded BICM systems.

中文翻译：

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LDPC码延迟位交错编码调制的设计与分析

本文研究了具有低密度奇偶校验 (LDPC) 码的延迟位交织编码调制 (DBICM) 的设计和性能。对于灰色标记的正方形 百万美元 元正交幅度调制 (QAM) 星座，我们研究了在固定最大延迟时隙数和给定信噪比下具有最大频谱效率的 DBICM 的最佳延迟方案。在分析 DBICM 的容量时，我们发现了两个重要的特性：由于延迟编码比特映射到传输符号的实部和虚部而导致的容量改进是相互独立的；一对具有相同比特信道容量的延迟编码比特的延迟方案导致等效的 DBICM 容量。使用这两个属性，我们有效地优化了任何统一 Gray-QAM 系统的延迟方案。此外，这两个特性通过位通道类型分类实现了关于不平等错误保护的高效 LDPC 码设计。而且，我们使用基于原型的外在信息传输图来联合优化 LDPC 码的度分布和信道分配，并提出一种约束渐进边增长算法来联合构建 DBICM 的 LDPC 码和比特交织器，同时考虑到不同比特信道的容量。仿真结果表明，设计的 LDPC 编码的 DBICM 系统明显优于 LDPC 编码的 BICM 系统。