• The KIPS Transactions:PartC
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• v.10C no.1
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• pp.27-32
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• 2003

An efficient soft-decision decoding algorithm for binary block codes it proposed. The proposed soft-decision decoding algorithm is implemented by a series of hard-decision decoding process. By the hard-decision decoding result, the candidate codewords are efficiently searched for A new decoding method, which prevents the missing of the candidate codeword, is proposed. Also, the method fir reducing complexity is developed. This method removes the practical complexity increase caused by the improved algorithm. There facts are confirmed by the simulation results for binary (63, 36) BCH code.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2010.11a
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• pp.282-284
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• 2010

1962년 Gallager에 의해서 처음 제안된 LDPC 부호는 터보부호(turbo codes)와 마찬가지로 Shannon의 채널용량 한계(channel capacity limit)에 가까운 성능을 보였지만 당시 기술력으로 구현이 불가능한 복잡도로 인해 오랫동안 잊혀져왔다. 1995년 Mackay 와 Neal은 이를 재발견하였고 간단한 확률적 복호법을 이용하여 LDPC 부호의 성능이 매우 우수함을 보였다. 또한 1997년 Mackay는 q>2일 때 LDPC 부호를 GF(q)상에서 구성할 경우에 성능이 더 좋아짐을 보였다. 본 논문에서는 이진 bit로 구성된 같은 길이의 정보 비트(information bit)를 통해 16-QAM 변조를 사용했을시 Binary LDPC 부호와 Non Binary LDPC 부호의 성능을 비교 분석하고, 최적의 성능을 가지는 LDPC 부호의 설계에 대해 제안한다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.12
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• pp.1742-1744
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• 2016

In this letter, we prove equivalence of the Binary perturbation and Afterburner LDPC decoder that are proposed for improving the decoding performance in short length LDPC codes.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.10A
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• pp.1576-1581
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• 2000

We investigated into the minimum distance of a primitive binary cyclic code C with a generator polynomial g(x)=$m_1(x)m_{d}(x)$. It is known that the necessary and sufficient condition for C to have minimum distance five is the fact that \ulcorner is an APN power function. In this paper we derived the new proof of minimum distance for the primitive binary cyclic codes with minimum distance five.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.115-137
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• 2018

Let $R_{u{^2},v^2,w^2,p}$ be a finite non chain ring ${\mathbb{F}}_p[u,v,w]{\langle}u^2,\;v^2,\;w^2,\;uv-vu,\;vw-wv,\;uw-wu{\rangle}$, where p is a prime number. This ring is a part of family of Frobenius rings. In this paper, we explore the structures of cyclic codes over the ring $R_{u{^2},v^2,w^2,p}$ of arbitrary length. We obtain a unique set of generators for these codes and also characterize free cyclic codes. We show that Gray images of cyclic codes are 8-quasicyclic binary linear codes of length 8n over ${\mathbb{F}}_p$. We also determine the rank and the Hamming distance for these codes. At last, we have given some examples.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.797-801
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• 2001

The purpose of this paper is to give an upper bound for A[n,4], the maximum number of codewords in a binary code of word length n with minimum distance 4 between codewords. We have improved upper bound for A[12k+11,4]. In this correspondence we prove $A[23,4]\leq173716$.

• Journal of Korea Multimedia Society
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• v.17 no.8
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• pp.961-967
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• 2014

Raptor codes are a class of rateless codes originally designed for binary erasure channels. This paper presents a compact set of mathematical expressions for iterative soft decoding of raptor codes. In addition, an early termination scheme is employed, and it is embedded in a single algorithm with the formula. In the proposed algorithm, the performance is enhanced by adopting iterative decoding, both in each inner and outer code and in the concatenated code itself between the inner and outer codes. At the same time, the complexity is reduced by applying an efficient early termination scheme. Simulation results show that our proposed method can achieve better performance with reduced decoding complexity compared to the conventional schemes.

• ETRI Journal
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• v.31 no.5
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• pp.518-524
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• 2009

Single parity check (SPC) product codes are simple yet powerful codes that are used to correct errors and/or recover erasures. The focus of this paper is to evaluate the performance of such codes under erasure scenarios and to develop a closed-form tight upper bound for the post-decoding erasure rate. Closed-form exact expressions are derived for up to seven erasures. Previously published closed-form bounds assumed that all unrecoverable patterns should contain four erasures in a square. Additional non-square patterns are accounted for in the proposed expressions. The derived expressions are verified using exhaustive search. Eight or more erasures are accounted for by using a bound. The developed expressions improve the evaluation of the recoverability of SPC product codes without the need for simulation or search algorithms, whether exhaustive or novel.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.5A
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• pp.527-536
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• 2004

A novel hybrid multiple access system, TD-BCDMA, where Binary CDMA that maintains a constant amplitude by clipping the summation of input signals multiplied by the orthogonal codes is transmitted over a TDMA frame structure, was Nosed. In every time slot of TDMA, binary CDMA modulated multiple channel signals are transmitted with the same waveform of TDMA. TD-BCDMA has all the advantages of TDMA. Flexible adjustment of the data transmission rate In demand is possible by adjusting the number of codes and time slots assigned to each user. This property was used to show an example of Ad Hoc network applications. To obtain a proper synchronization scheme for TD-BCDMA, the Receiver Operating Characteristics performance and the false alarm probability and false dismissal probability under various channel environment of two different schemes, a preamble scheme as in TDMA and a synchronization channel scheme as in CDMA were compared. It was proved that the preamble scheme is more practical and suitable than the synchronization channel scheme for the hybrid multiple access system.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.391-397
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• 2019

In this paper, we give a simple proof of the improved Johnson bound for A(n, d), the maximum number of codewords in a binary code of length n and minimum distance d, given by Mounits, Etzion and Litsyn.