In this paper, we propose fast bitmap search algorithms to reduce the computational complexity of transform-based vector quantization (VQ) techniques, which achieve better quality in reconstructed images than the ordinary VQ. By removing the unlikely codewords in each step, the bitmap search method, which starts from the most significant bitmap then the successive significant ones, can save more than 90% computation of the ordinary transformed VQ. By applying to the singular value decomposition (SVD) VQ as an example, theoretical analyses and simulation results show that the proposed bitmap search methods dramatically reduce the computation and achieve invisible distortion in the reconstructed images.

A compact residue arithmetic multiplier based on the radix-4 signed-digit arithmetic is presented. Conventional residue arithmetic circuits have been designed using binary number arithmetic system, but the carry propagation arises which limits the speed of arithmetic operations in residue modules. In this paper, two radix-4 signed-digit (SD) number representations, {-2,-1,0,1,2} and {-3,-2,-1,0,1,2,3}, are introduced. The former is used for the input and output, and the later for the inner arithmetic circuit of the presented multiplier. Integers 4p and 4p 1 are used as moduli of residue number system (RNS), where p is a positive integer and both circuits for partial product generation and sum of the partial products can be efficiently constructed by using the multiple-valued current-mode circuits. The modulo m addition, m=4p or m=4p 1, can be performed by an SD adder or an end-around-carry SD adder with the multiple-valued circuits and the addition time is independent of the word length of operands. The modulo m multiplier can be compactly constructed using a binary tree of the multiple-valued modulo m SD adders, and consequently the modulo m multiplication is performed in O(log p) time. The number of MOS transistors required in the presented residue arithmetic multiplier is about 86p2 + 66p.

To realize high-speed computations in a residue number system (RNS), an implementation method for residue arithmetic circuits using signed-digit (SD) number representation is proposed. Integers mp = (2p-1) known as Mersenne numbers are used as moduli, so that modulo mp addition can be performed by an end-around-carry SD adder and the addition time is independent of the word length of operands. Using a binary modulo mp SD adder tree, the modulo mp multiplication can be performed in a time proportional to log2p.

This paper deals with a high-speed digital circuit for discrete cosine transform (DCT). We propose a new algorithm that reduces the number of calculations for partial sum-of-products in the DCT and synthesize the small gate depth circuit of DCT by using carry-propagation-free adders based on redundant binary {1,0,1} representation. The gate depth is only half to one third that of the conventional algorithms with the same number of gates.

This paper deals with an efficient radix-2 divider design theory that uses carry-propagation-free adders based on redundant binary{1, 0, 1} representation. In order to compute the division fast, we look ahead to the next step quotient-digit selection embedded in the current partial remainder calculation. The solution is a function of the four most significant digits of the current partial remainder, when scaling the divisor in the range [1, 9/8). In gate depth, this result is better than the higher radix-4 case without the look-ahead quotient-digit selection and the design is simple.

A new design methodology is proposed and analyzed for the design of ternary logic systems. In the new ternary logic systems, no conversions among radices are required and only the two-state ternary literals associated with the ternary signals are transmitted in the whole system. With the new design methodology, the ternary systems can be realized by the dynamic CMOS logic circuits which are simple and fully compatible with those of the conventional binary logic circuits in process, power supply, and logic levels. A new dynamic differential logic called the CMOS Redundant Differential Logic (CRDL) is also developed to increase the logic flexibility and the circuit performance. Using the new design methodology and the CRDL circuits, the multiplier with redundant binary addition tree is designed in both non-pipelined and pipelined systems. The experimental chip has been fabricated and measured, which successfully verifies the correctness of the logic functions and the speed performance of the designed circuits.

This paper deals with the theory and design method of an efficient radix-4 divider using carry-propagation-free adders based on redundant binary {-1,0,+1} representation. The usual method of normalizing the divisor in the range [1/2,1) eliminates the advantages of using a higher radix than two, bacause many digits of the partial remainder are required to select the quotient digits. In the radix-4 case, it is shown that it is possible to select the quotient digits to refer to only the four (in the usual normalizing method it is seven) most significant digits of the partial remainder, by scaling the divisor in the range [12/8,13/8). This leads to radix-4 dividers more effective than radix-2 ones. We use the hyperstring graph representation proposed in Ref.(18) for redundant binary adders.