A K-user interleave-division multiple-access (IDMA) system with symbol-synchronous and equal-power users is considered. In this IDMA system, the spreading, interleaving, and multiple-access channel (MAC) are jointly considered as an equivalent channel, referred to as an IDMA channel. Given channel signal-to-noise ratio (SNR), the sum capacity of the IDMA channel is only determined by a K-user spread-interleave (SI) matrix. First, it is shown that to maximize the sum capacity of the IDMA channel, rows or columns of its K-user SI matrix should be pairwise orthogonal. The optimal K-user SI matrix is constructed. Second, for the IDMA system with each user employing the same spreading sequence followed by random interleaving, it is shown that, as the number of users approaches infinity, the sum capacity of the IDMA channel converges to a determinate value, which is achieved by a balanced spreading sequence. Moreover, when both the number of users and the data length approach infinity, this determinate value of sum capacity is achieved by an arbitrary spreading sequence. Furthermore, for a finite number of users, an optimal spreading sequence is derived by minimizing an expected column correlation of the K-user SI matrix. It shows that this optimal spreading sequence provides the maximum ergodic sum capacity.