• Proceedings of the IEEK Conference
• /
• 2000.11b
• /
• pp.297-300
• /
• 2000

This paper proposes a high-speed and area-efficient FFT algorithm and performs a hardware implementation. This algorithm, named by “Radix-4/2”, uses the feature of existing radix-2$^3$algorithm, It reduces the number of non-trivial multipliers in SFG to the ratio of 3 to 2 campared with radix-2 or radix-4 algorithm and radix-4/2 has also twice throughput as radix-2$^3$algorithm's. It is proved that FFT processor using the proposed algorithm and 64-point MDC pipeline architecture has twice throughput as radix-2$^3$algorithm's, and reduces areas by 25 percentages in contrast to radix-4 algorithm's.

• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.41 no.3
• /
• pp.55-64
• /
• 2004

In this paper, we propose an efficient FFT algorithm for high speed multimedia communication systems, and present its pipeline implementation results. Since the proposed algorithm is based on the radix-4 butterfly unit, the processing rate can be twice as fast as that based on the radix-2$^3$ algorithm. Also, its implementation is more area-efficient than the implementation from conventional radix-4 algorithm due to reduced number of nontrivial multipliers like using the radix-23 algorithm. In order to compare the proposed algorithm with the conventional radix-4 algorithm, the 64-point MDC pipelined FFT processor based on the proposed algorithm was implemented. After the logic synthesis using 0.6${\mu}{\textrm}{m}$ technology, the logic gate count for the processor with the proposed algorithm is only about 70% of that for the processor with the conventional radix-4 algorithm. Since the proposed algorithm can be achieve higher processing rate and better efficiency than the conventional algorithm, it is very suitable for the high speed multimedia communication systems such as WLAN, DAB, DVB, and ADSL/VDSL systems.

• Proceedings of the IEEK Conference
• /
• 2001.06a
• /
• pp.337-340
• /
• 2001

This paper presented a new structure of RSA cryptosystem using modified Montgomery algorithm and CSA(Carry Save Adder) tree. Montgomery algorithm was modified to a radix-4 modified Booth algorithm. By appling radix-4 modified Booth algorithm and CSA tree to modular multiplication, a clock cycle for modular multiplication has been reduced to (n＋3)/2 and carry propagation has been removed from the cell structure of modular multiplier. That is, the connection efficiency of full adders is enhanced.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.16 no.8
• /
• pp.5579-5585
• /
• 2015

In FFT(Fast Fourier Transform) implementation, DIT(Decimation-In-Time) and DIF (Decimation-In-Frequency) methods are mostly used. Among them, various DIF structures such as Radix-2/4/8 algorithm have been developed. Compared to the DIF, the DIT structures have not been investigated even though they have a big advantage producing a sequential output. In this paper, a butterfly structure for DIT Radix-8 algorithm is proposed. The proposed structure has smaller latency time because of Radix-8 algorithm in addition to the advantage of the sequential output. In case of 4096-point FFT implementation, the proposed structure has only 4 stages which shows the smaller latency time compared to the 12 stages of Radix-2 algorithm. The proposed butterfly can be used in FFT block required the sequential output and smaller latency time.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.12 no.2
• /
• pp.35-44
• /
• 2002

In this paper, an implementation method of RSA exponentiator based on Radix-$2^k$ modular multiplication algorithm is presented and verified. We use Booth receding algorithm to implement Radix-$2^k$ modular multiplication and implement radix-16 modular multiplier using 2K-byte memory and CSA(carry-save adder) array - with two full adder and three half adder delays. For high speed final addition we use a reduced carry generation and propagation scheme called pseudo carry look-ahead adder. Furthermore, the optimum value of the radix is presented through the trade-off between the operating frequency and the throughput for given Silicon technology. We have verified 1,024-bit RSA processor using Altera FPGA EP2K1500E device and Samsung 0.3$\mu\textrm{m}$ technology. In case of the radix-16 modular multiplication algorithm, (n+4+1)/4 clock cycles are needed and the 1,024-bit modular exponentiation is performed in 5.38ms at 50MHz.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.38A no.12
• /
• pp.1145-1147
• /
• 2013

There are two FFT(Fast Fourier Transform) algorithms, which are DIT(Decimation-In-Time) and DIF(Decimation-In- Frequency). Even the DIF algorithm is more widely used because of its various implementation architectures, the DIT structures have not been investigated. In this paper, the DIT Radix-4 algorithm is derived and its efficient butterfly structure is proposed for SoC(System on a Chip) implementation.

• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.49 no.3
• /
• pp.8-14
• /
• 2012

In this paper, a low-area FFT structure using $Radix-4^2$ algorithm is proposed. The large point FFT structure consists of cascade connection of the many stages. In implementation of large point FFT using $Radix-4^2$ algorithm, stages which number of different coefficients are only 3 appear in every 2 stages. For example, in the 4096-point FFT, the stages that number of different coefficients are 3 appear in stage 1, 3, and 5 among 6 stages. Multiplication block area of these 3 stages can be reduced using CSD(Canonic Signed Digit) and common sub-expression sharing techniques. Using the proposed structure, the 256-point FFT is implemented with the Verilog-HDL coding and synthesized by $1.971mm^2$ cell area in tsmc $0.18{\mu}m$CMOS library. This result shows 23% cell area reduction compared with the conventional structure.

• Proceedings of the IEEK Conference
• /
• 2002.06b
• /
• pp.173-176
• /
• 2002

This paper is about a high-speed MAC (multiplier and accumulator) design applying radix-4 and radix-8 Booth's algorithm at the same time. The optimized hybrid radix design for high speed MAC has taken advantage of both a radix-4 and a radix-8 architectures. A radix-4 architecture meets high-speed, but it takes much more power and chip area than a radix-8 architecture. A radix-8 architecture needs less power and chip area than the other, but it has a bottleneck of generating three times the multiplicand problem. An optimized hybrid architecture performs the radix-4 multiplication partially in parallel with the generation of three times the multiplicand for use of the radix-8 multiplication. It reduces the concerned bit width of multiplier in radix-8 multiplication.

• Proceedings of the IEEK Conference
• /
• 2002.06a
• /
• pp.125-128
• /
• 2002

This paper is about a high-speed MAC (multiplier and accumulator) design applying radix-4 and radix-8 Booth's algorithm at the same time. The optimized hybrid radix design for high speed MAC has taken advantage of both a radix-4 and a radix-8 architectures. A radix-4 architecture meets high-speed, but it takes much more power and chip area than a radix-8 architecture. A radix-8 architecture needs less power and chip area than the other, but it has a bottleneck of generating three times the multiplicand problem. An optimized hybrid architecture performs tile radix-4 multiplication partially in parallel with the generation of three times the multiplicand for use of tile radix-8 multiplication. It reduces the concerned bit width of multiplier in radix-8 multiplication.

• Journal of the Institute of Electronics Engineers of Korea SP
• /
• v.45 no.3
• /
• pp.103-110
• /
• 2008

In this paper, an efficient butterfly structure for 8K/2K-Point Radix-4 FFT algorithm using CORDIC(coordinate rotation digital computer) is proposed. It is shown that CORDIC can be efficiently used in twiddle factor calculation of the Radix-4 FFT algorithm. The Verilog-HDL coding results for the proposed CORDIC butterfly structure show 36.9% cell area reduction comparison with those of the conventional multiplier butterfly structure. Furthermore, the 8K/2K-point Radix-4 pipeline structure using the proposed butterfly and delay commutators is compared with other conventional structures. Implementation coding results show 11.6% cell area reduction. Due to its efficient processing scheme, the proposed FFT structure can be widely used in large size of FFT like OFDM Modem.