Sparse code multiple access (SCMA) is a promising non-orthogonal air-interface technology for its ability to support massive connections. In this paper, we design the multiuser codebook and the advanced decoding from the perspective of the theoretical capacity and the system feasibility. First, different from the lattice-based constellation in point-to-point channels, we propose a novel codebook for maximizing the constellation constrained capacity. We optimize a series of 1-D superimposed constellations to construct multi-dimensional codewords. An effective dimensional permutation switching algorithm is proposed to further obtain the capacity gain. Consequently, it shows that the performance of the proposed codebook approaches the Shannon limit and achieves significant gains over the other existing ones. Furthermore, we provide a symbol-based extrinsic information transfer tool to analyze the convergence of SCMA iterative detection, where the complex codewords are considered in modeling the a priori probabilities instead of assuming the binary inputs in previous literature. Finally, to approach the capacity, we develop a low-density parity-check code-based SCMA receiver. Most importantly, by utilizing the EXIT charts, we propose an iterative joint detection and decoding scheme with only partial inner iterations, which exhibits significant performance gain over the traditional one with separate detection and decoding.