• 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($m{\geq}0$), $n=6m+5(m{\geq}1)$.

• Proceedings of the IEEK Conference
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• 2004.08c
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• pp.645-648
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• 2004

In this paper, we drive a theoretical performance of complementary code keying (CCK) codes on additive white Gaussian noise (AWGN) channel. The CCK codes can be demodulated by the optimal maximum likelihood decoding method and sub-optimal correlation magnitude decoding algorithm. We calculate the bit error rate (BER) and symbol or codeword error rate (SER) of the CCK codes using the above mentioned two decoding algorithms. To derive the error performance, we use the weigh distributions and cross-correlation distributions of CCK codes.

• Proceedings of the IEEK Conference
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• 2000.11a
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• pp.165-168
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• 2000

The bit error rate(BER)of the data passed through Wideband-Code Division Multiple Access (W-CDMA) system with turbo-codes structure is presented. The performance of turbo-codes under W-CDMA system is estimated for various users and iteration numbers of decoding. The channel model is Additive White Gaussian Noise(AWGN) and Rayleigh fading channel. When iteration number increases, bit error probability of turbo-codes decreases. and when the number of users increase, bit error probability of turbo-codes increases.

• Journal of Communications and Networks
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• v.13 no.3
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• pp.205-210
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• 2011

This paper presents an approach to the construction of multiple-rate quasi-cyclic low-density parity-check (LDPC) codes. Parity-check matrices of the proposed codes consist of $q{\times}q$ square submatrices. The block rows and block columns of the parity-check matrix correspond to the hyperplanes (${\mu}$-fiats) and points in Euclidean geometries, respectively. By decomposing the ${\mu}$-fiats, we obtain LDPC codes of different code rates and a constant code length. The code performance is investigated in term of the bit error rate and compared with those of LDPC codes given in IEEE standards. Simulation results show that our codes perform very well and have low error floors over the additive white Gaussian noise channel.

• Journal of Communications and Networks
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• v.11 no.5
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• pp.455-463
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• 2009

We consider the challenges of finding good puncturing patterns for rate-compatible low-density parity-check code (LDPC) codes over additive white Gaussian noise (AWGN) channels. Puncturing is a scheme to obtain a series of higher rate codes from a lower rate mother code. It is widely used in channel coding but it causes performance is lost compared to non-punctured LDPC codes at the same rate. Previous work, considered the role of survived check nodes in puncturing patterns. Limitations, such as single survived check node assumption and simulation-based verification, were examined. This paper analyzes the performance according to the role of multiple survived check nodes and multiple dead check nodes. Based on these analyses, we propose new algorithm to find a good puncturing pattern for LDPC codes over AWGN channels.

• ETRI Journal
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• v.29 no.3
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• pp.381-389
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• 2007

In this paper we propose a graph-theoretic method based on linear congruence for constructing low-density parity check (LDPC) codes. In this method, we design a connection graph with three kinds of special paths to ensure that the Tanner graph of the parity check matrix mapped from the connection graph is without short cycles. The new construction method results in a class of (3, ${\rho}$)-regular quasi-cyclic LDPC codes with a girth of 12. Based on the structure of the parity check matrix, the lower bound on the minimum distance of the codes is found. The simulation studies of several proposed LDPC codes demonstrate powerful bit-error-rate performance with iterative decoding in additive white Gaussian noise channels.

• ETRI Journal
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• v.26 no.5
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• pp.432-436
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• 2004

In this paper, we propose the modified uniformly most powerful (UMP) belief-propagation (BP)-based decoding algorithm which utilizes multiplicative and additive factors to diminish the errors introduced by the approximation of the soft values given by a previously proposed UMP BP-based algorithm. This modified UMP BP-based algorithm shows better performance than that of the normalized UMP BP-based algorithm, i.e., it has an error performance closer to BP than that of the normalized UMP BP-based algorithm on the additive white Gaussian noise channel for low density parity check codes. Also, this algorithm has the same complexity in its implementation as the normalized UMP BP-based algorithm.

• Proceedings of the KIEE Conference
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• 2005.10a
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• pp.173-175
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• 2005

Two-dimensional orthogonal variable spreading codes are presented for multiplexing of forward link in direct sequence code division multiple access (DS-CDMA) multiple antennas system And the results of code generation and simulation of 2 dimensional orthogonal variable spreading factors on Jacket matrices are also be investigated. The bit error rate(BER) performance under a multi-user environment for the additive white Gaussian noise (AWGN) channel demonstrated that the proposed scheme could provide flexible rates and lower correlation values