This paper focuses on coding, retransmission, and Adaptive Modulation and Coding (AMC) for Beyond the Fifth Generation (B5G) and the Sixth Generation (6G) mobile communication scenarios. Firstly, for coding, we propose a coupled coding scheme to enhance the 5G Low-Density Parity-Check (LDPC) codes, named Block Markov Superposition Transmission of 5G LDPC (BMST-5G-LDPC) codes. Specifically, a portion (denoted as the superposition fraction $\alpha$) of bits of the previous 5G LDPC coded block is superimposed onto the current coded block, resulting in the current transmitted codeword. To optimize the superposition fraction, we propose a generalized EXtrinsic Information Transfer (EXIT) chart analysis, which can efficiently guide the optimization of $\alpha$, as consistent with the simulation. Secondly, for retransmission, we introduce a new Hybrid Automatic Repeat reQuest (HARQ) scheme, in which the retransmitted data are obtained by multiplying the erroneous coded blocks or coded block groups with the Low-Density Generator Matrix (LDGM), called LDGM-HARQ. The key issue lies in the optimization of the LDGM, with an important parameter being the column weight of the matrix. Similarly, we present an EXIT chart analysis to optimize the key matrix, and the simulation results confirm the effectiveness of the analysis. Meanwhile, we also present the throughput analysis based on the renewal-reward theorem to describe the improvement of the LDGM-HARQ over the conventional HARQ scheme. Thirdly, for AMC, by employing the proposed coding and HARQ scheme, we present the throughput performance combined with the link adaption, further revealing the performance gains of the proposed scheme compared to the 5G standard.