The integration of multicarrier modulation and multiple-input-multiple-output (MIMO) is critical for reliable transmission of wireless signals in complex environments, which significantly improve spectrum efficiency. Existing studies have shown that popular orthogonal time frequency space (OTFS) and affine frequency division multiplexing (AFDM) offer significant advantages over orthogonal frequency division multiplexing (OFDM) in uncoded doubly selective channels. However, it remains uncertain whether these benefits extend to coded systems. Meanwhile, the information-theoretic limit analysis of coded MIMO multicarrier systems and the corresponding low-complexity receiver design remain unclear. To overcome these challenges, this paper proposes a multi-slot cross-domain memory approximate message passing (MS-CD-MAMP) receiver as well as develops its information-theoretic (i.e., achievable rate) limit and optimal coding principle for MIMO-multicarrier modulation (e.g., OFDM, OTFS, and AFDM) systems. The proposed MS-CD-MAMP receiver can exploit not only the time domain channel sparsity for low complexity but also the corresponding symbol domain constellation constraints for performance enhancement. Meanwhile, limited by the high-dimensional complex state evolution (SE), a simplified single-input single-output variational SE is proposed to derive the achievable rate of MS-CD-MAMP and the optimal coding principle with the goal of maximizing the achievable rate. Numerical results show that coded MIMO-OFDM/OTFS/AFDM with MS-CD-MAMP achieve the same maximum achievable rate in doubly selective channels, whose finite-length performance with practical optimized low-density parity-check (LDPC) codes is only 0.5 $\sim$ 1.8 dB away from the associated theoretical limit, and has 0.8 $\sim$ 4.4 dB gain over the well-designed point-to-point LDPC codes.

翻译：多载波调制与多输入多输出技术的融合对于复杂环境中无线信号的可靠传输至关重要，可显著提升频谱效率。现有研究表明，在非编码的双选择性信道中，主流的正交时频空调制与仿射频分复用相较于正交频分复用具有显著优势。然而，这些优势能否延续至编码系统尚不明确。同时，编码MIMO多载波系统的信息论极限分析及相应的低复杂度接收机设计仍有待探索。为应对这些挑战，本文提出一种多时隙跨域记忆近似消息传播接收机，并针对MIMO多载波调制系统（如OFDM、OTFS与AFDM）建立了其信息论极限（即可达速率）与最优编码准则。所提出的MS-CD-MAMP接收机既能利用时域信道稀疏性以降低复杂度，又能结合符号域星座约束以提升性能。同时，受限于高维复数状态演化分析的复杂性，本文提出简化的单输入单输出变分状态演化方法，用以推导MS-CD-MAMP的可达速率及以最大化可达速率为目标的最优编码准则。数值结果表明，采用MS-CD-MAMP的编码MIMO-OFDM/OTFS/AFDM系统在双选择性信道中可实现相同的最大可达速率，其采用实际优化低密度奇偶校验码的有限长性能距理论极限仅0.5 $\sim$ 1.8 dB，且较精心设计的点对点LDPC码方案有0.8 $\sim$ 4.4 dB的性能增益。