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In power control, the convergence rate is one of the most important criteria that can determine the practical applicability of a given algorithm. The convergence rate of power control is especially important when propagation and traffic conditions are changing rapidly. To track these changes, the power control algorithm must converge quickly. The purpose of this paper is to generalize the existing power control framework such that we can utilize partially known link gain information in improving the convergence speed. For the purpose, block power control (BPC) is suggested with its convergence properties. BPC is centralized within each block in the sense that it exchanges link gain information within the same block. However, it is distributed in a block-wise manner, and no information is exchanged between different blocks. Depending on availability of link gain information, a block can be any set of users, and can even consist of a single user. Computational experiments are carried out on a direct-sequence code-division multiple-access system, illustrating how BPC utilizes available link gain information in increasing the convergence speed of the power control.