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Multicarrier-low-density spreading multiple access (MC-LDSMA) is a novel non-orthogonal multiple access scheme, which exploits a multidimensional codebook based on the sparse spreading technique. In this letter, instead of assuming the ideal Gaussian inputs, we contribute to design the sparse spreading codebook with the finite alphabet inputs in an information-theoretic framework. Single user mutual information (SMI) for the system with a generic detection is first derived. Different from the traditional method for maximizing the sum rate, we propose a fairness balanced criterion to maximize the minimal SMI in Gaussian multiple access channels. The modified multistart interior-point algorithm is proposed to obtain the optimal codebook. With the proposed codebook, MC-LDSMA achieves significant performance gains over the previously known schemes in terms of the SMI and bit-error rate.