• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1235-1255
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• 2019

In this paper, we introduce SR-additive codes as a generalization of the classes of ${\mathbb{Z}}_{p^r}{\mathbb{Z}}_{p^s}$ and ${\mathbb{Z}}_2{\mathbb{Z}}_2[u]$-additive codes, where S is an R-algebra and an SR-additive code is an R-submodule of $S^{\alpha}{\times}R^{\beta}$. In particular, the definitions of bilinear forms, weight functions and Gray maps on the classes of ${\mathbb{Z}}_{p^r}{\mathbb{Z}}_{p^s}$ and ${\mathbb{Z}}_2{\mathbb{Z}}_2[u]$-additive codes are generalized to SR-additive codes. Also the singleton bound for SR-additive codes and some results on one weight SR-additive codes are given. Among other important results, we obtain the structure of SR-additive cyclic codes. As some results of the theory, the structure of cyclic ${\mathbb{Z}}_2{\mathbb{Z}}_4$, ${\mathbb{Z}}_{p^r}{\mathbb{Z}}_{p^s}$, ${\mathbb{Z}}_2{\mathbb{Z}}_2[u]$, $({\mathbb{Z}}_2)({\mathbb{Z}}_2+u{\mathbb{Z}}_2+u^2{\mathbb{Z}}_2)$, $({\mathbb{Z}}_2+u{\mathbb{Z}}_2)({\mathbb{Z}}_2+u{\mathbb{Z}}_2+u^2{\mathbb{Z}}_2)$, $({\mathbb{Z}}_2)({\mathbb{Z}}_2+u{\mathbb{Z}}_2+v{\mathbb{Z}}_2)$ and $({\mathbb{Z}}_2+u{\mathbb{Z}}_2)({\mathbb{Z}}_2+u{\mathbb{Z}}_2+v{\mathbb{Z}}_2)$-additive codes are presented.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.341-357
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• 2018

We examine various dualities over the fields of even orders, giving new dualities for additive codes. We relate the MacWilliams relations and the duals of ${\mathbb{F}}_{2^{2s}}$ codes for these various dualities. We study self-dual codes with respect to these dualities and prove that any subgroup of order $2^s$ of the additive group is a self-dual code with respect to some duality.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.729-740
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• 2018

In this paper, we define near-minimal shadow and study the existence problem of extremal Type I additive self-dual codes over GF(4) with near-minimal shadow. We prove that there is no such codes if the code length n = 6m+1($m{\geq}0$), $n=6m+5(m{\geq}1)$.

• Journal of IKEEE
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• v.11 no.4
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• pp.198-204
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• 2007

For parallel and serially concatenated trellis coded modulation (TCM), improved iterative decoding schemes with a simple mechanism are proposed and their performances are compared with those of conventional decoding schemes. Simulation results have shown that the proposed schemes have provided a considerable decoding gain in additive white Gaussian noise (AWGN) channels and Rayleigh fading channels, even if they can be implemented by a simple modification of conventional decoding algorithms.

• Journal of Communications and Networks
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• v.8 no.3
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• pp.257-266
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• 2006

The powerful benefits of multi-antenna systems can be obtained by cooperative communications among users in multiple access environments without the need for physical arrays. This paper studies a novel cooperative signaling strategy that achieves high performance and low implementation complexity for synchronous code division multiple access (CDMA) wireless mobile networks. The validity of the proposed strategy under slow flat Rayleigh fading channel plus additive white Gaussian noise (AWGN) is verified through closed-form error probability expressions and MonteCarlo simulations. A variety of analytical results reveal that the new cooperative strategy significantly outperforms direct transmission subject to the same spectral efficiency and transmit power constraint.

• Journal of Communications and Networks
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• v.8 no.3
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• pp.306-312
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• 2006

This paper studies theoretically the bit error rate (BER) performance of cooperative transmission using space-time block code (STBC) in a fully distributed manner. Specifically, we first propose a STBC-based cooperative signaling structure to make the cooperation of three single-antenna terminals possible. Then, we derive the closed-form BER expressions for both cooperation and noncooperation schemes under flat Rayleigh fading channel plus additive white Gaussian noise (AWGN). The validity of these expressions is verified by Monte-Carlo simulations. A variety of numerical and simulation results reveal that the cooperative transmission achieves higher diversity gain and better performance than the direct transmission for the same total transmit power.

• Proceedings of the Korea Contents Association Conference
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• 2003.11a
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• pp.303-307
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• 2003

In this paper, the W(ultra widebend) system is used for high speed transmission applying BPSK(Binary Phase Shift Keying) and QPSK (Quadrature Phase Shift Keying), and utilizing the convolution coding with code rate, 1/2 and constraint length, K=7 in order to reduce the bit error rate. And the performance of system is analyzed in the AWGN(Additive White Gaussian Noise) channel environment by using the Viterbi decoding algorithm and adopting the time-hopping sequence as a multiple access method in order to avoid the multiuser interference.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.28A no.11
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• pp.855-865
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• 1991

A simple method for analysis of serial search burst-format direct-sequence spread-spectrum (DS-SS) code acquisition system had been recently proposed, and therein, the effect of the code autocorrelation sidelobes on the performance of DS-SS code acquisition system has been assessed [4],[5]. In this paper, a new hybrid scheme which combines the serial search with maximum likelihood search is proposed to eliminate the deleterious effect of code autocorrelation sidelobes, and the performance is analyzed for the additive withe Gaussian noise (AWGN) channels. To analyze the performance of this system, we have generalized the method used in [4],[5] to arbitrary burst-format DS-SS acquisition schemes. The results show that a new hybrid scheme has good immunity against the effect of code autocorrelation sidelobes. Thevalidity of the presented approach has been confirmed form the results of simulation.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.7C
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• pp.587-593
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• 2010

In this paper we design an irregular low-density parity-check (LDPC) code for multiple-input multiple-output (MIMO) system, using a simple extrinsic information transfer (EXIT) chart method. The MIMO systems considered are optimal maximum a posteriori probability (MAP) detector. The MIMO detector and the LDPC decoder exchange soft information and form a turbo iterative receiver. The EXIT charts are used to obtain the edge degree distribution of the irregular LDPC code which is optimized for the MIMO detector. It is shown that the performance of the designed LDPC code is better than that of conventional LDPC code which was optimized for either the Additive White Gaussian Noise (AWGN) channel or the MIMO channel.

• Korean Journal of Optics and Photonics
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• v.13 no.5
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• pp.435-441
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• 2002

In this paper, we propose an optimal 2-dimensional construction algorithm of a code family for a high-speed optical code division multiple access network. The optimal 2-D code family generated by search algorithm has better spectrum efficiency than previous codes, having relatively many code sets with short code length and the same or lower BER. Using the optimal 2-D code, OCDMA systems make it possible to utilize the spectrum more efficiently than WDM systems. The probability of bit error for high-speed OCDMA transmissions is calculated as a function of the number of users in the presence of receiver and shot noise(additive white Gaussian noise).