This paper presents the algorithm and very-large-scale integration (VLSI) architecture of a high-throughput and highly efficient independent component analysis (ICA) processor for self-interference cancellation (SIC) in in-band full-duplex (IBFD) systems. This is the first VLSI architecture reported in the literature based on the state-of-the-art entropy bound minimization (EBM) approach. A novel ICA algorithm is presented in this paper with momentum gradient descent optimization. Simulation results show that the number of iterations for the proposed algorithm is significantly reduced compared to the conventional ICA algorithms. Furthermore, a novel early-distribution estimation scheme is proposed in the designed ICA processor to compute multiple distribution functions with low latency and low complexity. The processing flow and the efficiency for the hardware utilization are specifically designed so that the processing speed is maximized with minimum employment of hardware components. The proposed ICA processor is designed and implemented based on the application-specific-integrated circuit (ASIC) flow. The post-layout estimations show that compared with the conventional EBM-based scheme, the proposed design improves the throughput and efficiency by 30x. In addition, compared to prior designs shown in the literature, the proposed ICA processor also demonstrates a significant enhancement in terms of throughput and efficiency.