An Improved Signed Digit Representation Approach for Constant Vector Multiplication

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In this brief, the multiplier-free implementation of the constant vector multiplication is reexamined. A novel improved signed digit representation technique is proposed to overcome the two main drawbacks of the current multiplier-free techniques: 1) computational redundancy and 2) circuit irregularity. The fundamental difference between the proposed technique and the existing multiplier-free techniques is a novel optimization framework based on vector decomposition. The constant vector is decomposed into two terms: a “public” vector and a “private” matrix which consist of the public operations shared by all of the entries and the private operations of each individual entry, respectively. In this way, the overall data flow can be divided into two regular steps: multiplied by the “public” vector first and then by the “private” matrix. The computational complexity reduction task is then achieved by minimizing the length of the “public” vector and the number of operations in the “private” matrix. Experimental results demonstrate that the proposed technique outperforms the existing multiplier-free techniques in fewer operations and more regular circuit structure.