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This paper presents an efficient acoustic echo cancellation (AEC) scheme based on reduced-rank interpolated adaptive filtering with parallel decimation, motivated by diversity techniques developed in wireless communications. The proposed scheme jointly optimizes an interpolation filter, a decimator unit and a reduced-rank filter in such a way that the output error is minimized, leading to very substantial improvements of the mean squared error performance. With a practical choice of parameters in AEC, the total computational complexity of the proposed scheme is approximately half of the one of the NLMS algorithm. The numerical examples demonstrate that the proposed algorithm offers very significant reduction in mean squared error performance.