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In this paper, we present an efficient distributed-arithmetic (DA) formulation for the implementation of block least mean square (BLMS) algorithm. The proposed DA-based design uses a novel look-up table (LUT)-sharing technique for the computation of filter outputs and weight-increment terms of BLMS algorithm. Besides, it offers significant saving of adders which constitute a major component of DA-based structures. Also, we have suggested a novel LUT-based weight updating scheme for BLMS algorithm, where only one set of LUTs out of M sets need to be modified in every iteration, where N=ML, N, and L are, respectively, the filter length and input block-size. Based on the proposed DA formulation, we have derived a parallel architecture for the implementation of BLMS adaptive digital filter (ADF). Compared with the best of the existing DA-based LMS structures, proposed one involves nearly L/6 times adders and L times LUT words, and offers nearly L times throughput of the other. It requires nearly 25% more flip-flops and does not involve variable shifters like those of existing structures. It involves less LUT access per output (LAPO) than the existing structure for block-size higher than 4. For block-size 8 and filter length 64, the proposed structure involves 2.47 times more adders, 15% more flip-flops, 43% less LAPO than the best of existing structures, and offers 5.22 times higher throughput. The number of adders of the proposed structure does not increase proportionately with block size; and the number of flip-flops is independent of block-size. This is a major advantage of the proposed structure for reducing its area delay product (ADP); particularly, when a large order ADF is implemented for higher block-sizes. ASIC synthesis result shows that, the proposed structure for filter length 64, has almost 14% and 30% less ADP and 25% and 37% less EPO than the best of the existing structures for block- size 4 and 8, respectively.