Fixed-width CSD multipliers with minimum mean square error

Many multimedia and DSP applications require fixed-width multipliers, in which input data and output results have the same bit width. In this paper we investigate fixed-width multipliers where one of the input operand is a constant, encoded using canonic signed digit (CSD) representation. This is a very important case in many practical applications such as the calculation of Fast Fourier Transform. In the paper we derive in closed form the expression of the compensation function giving the minimum mean square error for CSD fixed-width multiplier. On the basis of this analytical result, we propose a hardware efficient implementation of the multiplier. Fixed width CSD multipliers implemented with the approach presented in this paper are accurate and can be implemented by using a simple partial-product reduction tree followed by a fast adder, without requiring additional look-up tables. The proposed approach is general and is well suited for implementation in circuit synthesizers. Implementation results in 90 nm technology are presented, to demonstrate the effectiveness of the proposed technique.