• Proceedings of the IEEK Conference
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• 2000.07a
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• pp.167-170
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• 2000

This paper describes a novel multi-operand radix-2 signed-digit(SD) adder. The novel multi-operand addition algorithm can eliminate carry propagation chain by dividing the input operands into even place part and odd place part, and adding them each. The multi-operand adder with this algorithm can add six operands in parallel, and is faster than the ordinary method of SD adder binary tree. A hardware model for proposed adder is shown which is implemented by the current-mode MOSFET circuit technology. Simulations have been made by SPICE in order to verify the function of the proposed circuit.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.39 no.12
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• pp.1062-1070
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• 2002

In this paper, variable radix-two multibit coding algorithm is presented and applied in the implementation of discrete cosine transform(DCT) and inverse discrete cosine transform(IDCT). Variable radix-two multibit coding means the 2k SD (signed digit) representation of overlapped multibit scanning with variable shift method. SD represented by 2k generates partial products, which can be easily implemented with shifters and adders. This algorithm is most powerful for the hardware implementation of DCT/IDCT with constant coefficient matrix multiplication. This paper introduces the suggested algorithm, it's proof and the implementation of DCT/IDCT The implemented IDCT chip with 8 PEs(Processing Elements) and one transpose memory runs at a tate of 400 Mpixels/sec at 54MHz frequency for high speed parallel signal processing, and it's verified in HDTV and MPEG decoder.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.11
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• pp.2249-2254
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• 1994

An observation which is useful for hardware implementation of programmable FIR filters with powers-of two coefficients (2PFIR filters) is made. Specifically, it is shown that the exponents of filter coefficients representable by the canonical signed digit(CSD) code with M ternary digits can be chosen from some subsets of {0, 1, $\cdots$, M-1}. This observation naturally leads to 2PFIR filters with shorter shifters whose length is strictly less than M and, as a consequence, leads to an efficient hardware structure fo programmable 2PFIR filtering. In addition, we present some experimental results indicating that the shifters of 2PFIR filters can be shortened further in some cases.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.2 no.1
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• pp.37-42
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• 2009

The digital filter is essential element in digital signal processing area. It needs a high computational burden caused by multiplying and adding. The multiplier in digital filter is a dominant element, which occupies an wide area at the field of VLSI design, needs high power-consuming and also decides critical path that affects to filter performance. In this paper we proposed the simultaneous transform method which is represented 2's complementary representation to CSD and MSD representation to solve a complexity problem and to improve a computational speed. The performance of proposed method was implemented in VHDL and applied to an digital filters, was evaluated the decreasing of critical path delay.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.38 no.11
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• pp.810-820
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• 2001

Conventional binary adder requires a carry propagation to the most significant bit, and leads to serial addition. However, optical adder using a modified signed digit(MSD) number system has been Proposed to reduce the carry propagation chain encountered in binary adder. In this paper, in order to minimize the number of symbolic substitution(SS) rules, nine input patterns were divided into five groups of the same addition results. For recognizing the input reference patterns, serial connections of joint spatial encoded patterns and masks without any other spatial operations are used.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.12 no.3
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• pp.1387-1394
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• 2011

In this paper, a low-area symbol timing offset synchronization structure for WLAN Modem is proposed. Using CSD(Canonic Signed Digit) coefficients and CSS(Common Sub-expression Sharing) technique for the filter implementation, efficient structure for multiplication block can be obtained. Function simulation for proposed structure is done by using the preamble with timing offset. Through Verilog-HDL coding and synthesis, it is shown that the proposed symbol timing offset synchronization structure can be implemented with low-area semiconductor.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.1C
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• pp.119-128
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• 2004

In this paper, a low-power 8-point DCT structure is proposed using add and shift operations. Proposed structure adopts 4 cycles for complete 8-point DCT in order to minimize size of hardware and to enable high-speed processing. In the structure, hardware for the first cycle can be shared in the next 3 cycles since all columns in the DCT coefficient matrix are common except sign. Conventional DCT structures implemented with only add and shift operation use CSD(Canonic Signed Digit) form coefficients to reduce the number of adders. To reduce the number of adders further, we propose a new structure using common sub-expression sharing techniques. With this techniques, the proposed 8-point DCT structure achieves 19.5% adder reduction comparison to the conventional structure using only CSD coefficient form.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.41 no.5
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• pp.283-290
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• 2004

In this paper, a low-power structure for 512 tap FIR filter in MPEG audio algorithm is proposed. By using CSD(Canonic Signed Digit) form filter coefficients and maximum sharing of input signal sample, it is shown that the number of adders of proposed structure can be minimized. To minimize the number of adders, the proposed structure utilizes the 4 steps of sharing, i.e., common input sharing, linear phase symmetric filter coefficient sharing, block sharing for common input, and common sub-expression sharing. Through Verilog-HDL coding, it is shown that reduction rates in the implementation area and relative power consumption of the proposed structure are 60.3% and 93.9% respectively, comparison to those of the conventional multiplier structure.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.7
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• pp.3455-3474
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• 2018

As a unique form of signed-digit representation, non-adjacent form (NAF) minimizes Hamming weight by removing a stream of non-zero bits from the binary representation of positive integer. Thanks to this strong point, NAF has been used in various applications such as cryptography, packet filtering and so on. In this paper, to improve the NAF conversion speed of the $NAF_w$ algorithm, we propose a new NAF conversion algorithm, called w-bit Shifting Non-Adjacent Form($SNAF_w$), where w is width of scanning window. By skipping some unnecessary bit comparisons, the proposed algorithm improves the NAF conversion speed of the $NAF_w$ algorithm. To verify the excellence of the $SNAF_w$ algorithm, the $NAF_w$ algorithm and the $SNAF_w$ algorithm are implemented in the 8-bit microprocessor ATmega128. By measuring CPU cycle counter for the NAF conversion under various input patterns, we show that the $SNAF_2$ algorithm not only increases the NAF conversion speed by 24% on average but also reduces deviation in the NAF conversion time for each input pattern by 36%, compared to the $NAF_2$ algorithm. In addition, we show that $SNAF_w$ algorithm is always faster than $NAF_w$ algorithm, regardless of the size of w.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.4A
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• pp.324-329
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• 2002

In the high-speed/low-power digital filter applications like wireless communication systems, canonical signed digit(CSD) linear phase finite impulse response(FIR) filter structures are widely investigated. In this paper, we propose a high-speed/low-power CSD linear phase FIR filter structure using vertical common sub-expression. In the conventional linear phase CSD filter, horizontal common sub-expressions are utilized due to the inherent horizontal common sub-expression of symmetrical filter coefficients. We use the fact that their MSBs are also equal since adjacent filter coefficients have similar values in the linear phase filter Through the examples, it is shown that our proposed structure is more efficient in case that precision of implementation is lower, and tap length are longer.