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In this paper, a practical pipelined K-best lattice decoder featuring efficient operation over infinite complex lattices is proposed. This feature is a key element that enables it to operate at a significantly lower complexity than currently reported schemes. The main innovation is a simple means of expanding/visiting the intermediate nodes of the search tree on-demand, rather than exhaustively or approximately, and also directly within the complex-domain framework. In addition, a new distributed sorting scheme is developed to keep track of the best candidates at each search phase; the combined expansion and sorting cores are able to find the K best candidates in just K clock cycles. Its support of unbounded infinite lattice decoding distinguishes our work from previous K-best strategies and also allows its complexity to scale sub-linearly with modulation order. Since the expansion and sorting cores cooperate on a data-driven basis, the architecture is well-suited for a pipelined parallel VLSI implementation of the proposed K-best lattice decoder. Comparative results demonstrating the promising performance, complexity and latency profiles of our proposal are provided in the context of the 4x4 MIMO detection problem.