• 대한수학회지
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• 제44권5호
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• pp.1139-1162
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• 2007

We examine the main linear coding theory problem and study the structure of optimal linear codes over the ring ${\mathbb{Z}}_m$. We derive bounds on the maximum Hamming weight of these codes. We give bounds on the best linear codes over ${\mathbb{Z}}_8$ and ${\mathbb{Z}}_9$ of lengths up to 6. We determine the minimum distances of optimal linear codes over ${\mathbb{Z}}_4$ for lengths up to 7. Some examples of optimal codes are given.

• 대한수학회보
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• 제51권4호
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• pp.1175-1186
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• 2014

We construct new binary optimal self-dual codes of length 50. We develop a construction method for binary self-dual codes with a fixed-point-free automorphism of order 2. Using this method, we find new binary optimal self-dual codes of length 52. From these codes, we obtain Lee-optimal self-dual codes over the ring $\mathbb{F}_2+u\mathbb{F}_2$ of lengths 25 and 26.

• 대한수학회보
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• 제59권6호
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• pp.1557-1565
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• 2022

In this paper, Glift codes, generalized lifted polynomials, matrices are introduced. The advantage of Glift code is "distance preserving" over the ring R. Then optimal codes can be obtained over the rings by using Glift codes and lifted polynomials. Zero divisors are classified to satisfy "distance preserving" for codes over non-chain rings. Moreover, Glift codes apply on MDS codes and MDS codes are obtained over the ring 𝓡 and the non-chain ring 𝓡_e,s.

• 대한수학회보
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• 제52권6호
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• pp.2011-2023
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• 2015

This paper determines the structures of one-homogeneous weight codes over finite chain rings and studies the algebraic properties of these codes. We present explicit constructions of one-homogeneous weight codes over finite chain rings. By taking advantage of the distance-preserving Gray map defined in [7] from the finite chain ring to its residue field, we obtain a family of optimal one-Hamming weight codes over the residue field. Further, we propose a generalized method that also includes the examples of optimal codes obtained by Shi et al. in [17].

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2004년도 학술대회지
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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.

• 한국통신학회논문지
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• 제31권9C호
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• pp.825-830
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• 2006

Capacity-approaching codes using iterative decoding have been the main subject of research activities during past decade. Especially, LDPC codes show the best asymptotic performance and density evolution has been used as a powerful technique to analyze and design good LDPC codes. In this paper, we apply density evolution with a Gaussian approximation to the concatenated zigzag (CZZ) codes by considering both flooding and two-way schedulings. Based on this density evolution analysis, the threshold values are computed for various CZZ codes and the optimal structure of CZZ codes for various code rates are obtained. Also, simulation results are provided to conform the analytical results.

• 한국통신학회논문지
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• 제25권6B호
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• pp.1100-1105
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• 2000

현대의 레이더 펄스 압축기술로 가장 널리 사용되고 있는 방식은 바커코드를 사용하여 matched filter로 레이더 신호를 처리하는 상관처리(correlation processing)이다. 그러나 이 방식의 경우 탐지 감도를 높여 주는 장점이 있지만, 환경에 따라서 range-sidelobe가 발생하여 레이더의 성능을 낮추게 된다. 본 논문에서는 상관처리방식에 추가적인 처리로 sidelobe를 제거하는 최적처리 방법을 제안하고 Doppler shift가 존재할 때의 성능을 평가한다. 그리고 제안된 알고리즘 환경에서 최적의 이진 코드를 개발하고 이를 Barker 코드를 사용한 전통적인 상관처리방식의 경우와 비교.분석한다. 도플러 변이가 존재할 때, 최적 코드를 사용하여 최적 처리하는 방식이 바커코드를 사용한 전통적인 처리방법보다 레이더의 성능을 향상시킴을 보여줄 것이다.

• 대한수학회지
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• 제59권1호
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• pp.193-204
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• 2022

We present construction methods for free self-orthogonal (self-dual or Type II) codes over ℤ₄[v]/〈v² + 2v〉 which is one of the finite commutative local non-chain Frobenius rings of order 16. By considering their Gray images on ℤ₄, we give a construct method for a code over ℤ₄. We have some new and optimal codes over ℤ₄ with respect to the minimum Lee weight or minimum Euclidean weight.

• ETRI Journal
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• 제40권3호
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• pp.291-302
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• 2018

The deployment of an incremental hybrid decode-amplify and forward relaying scheme is a promising and superior solution for cellular networks to meet ever-growing network traffic demands. However, the selection of a suitable relaying protocol based on the signal-to-noise ratio threshold is important in realizing an improved quality of service. In this paper, an incremental hybrid relaying protocol is proposed using polar codes. The proposed protocol achieves a better performance than existing turbo codes in terms of capacity. Simulation results show that the polar codes through an incremental hybrid decode-amplify-and-forward relay can provide a 38% gain when ${\gamma}_{th(1)}$ and ${\gamma}_{th(2)}$ are optimal. Further, the channel capacity is improved to 17.5 b/s/Hz and 23 b/s/Hz for $2{\times}2$ MIMO and $4{\times}4$ MIMO systems, respectively. Monte Carlo simulations are carried out to achieve the optimal solution.

• 한국통신학회논문지
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• 제41권10호
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• pp.1176-1178
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• 2016

본 논문에서는 패리티 검사 행렬에 기반하여 부분접속수가 2인 이진 부분접속 복구 부호의 생성법을 제안한다. 제안하는 부호는 항상 최소거리 6을 갖는다. 이 부호는 부호의 길이와 최소거리가 주어졌을 때 부분접속수가 2인 부호가 가질 수 있는 최대의 차원을 갖는다는 관점에서 최적이다.