• KSII Transactions on Internet and Information Systems (TIIS)
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• 제15권9호
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• pp.3458-3481
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• 2021

Existing methods for blind identification of linear block codes without a candidate set are mainly built on the Gauss elimination process. However, the fault tolerance will fall short when the intercepted bit error rate (BER) is too high. To address this issue, we apply the reverse algebra approach and propose a novel "two-step-screening" algorithm by solving the linear error equations on the binary Galois field, or GF(2). In the first step, a recursive matrix partition is implemented to solve the system linear error equations where the coefficient matrix is constructed by the full codewords which come from the intercepted noisy bitstream. This process is repeated to derive all those possible parity-checks. In the second step, a check matrix constructed by the intercepted codewords is applied to find the correct parity-checks out of all possible parity-checks solutions. This novel "two-step-screening" algorithm can be used in different codes like Hamming codes, BCH codes, LDPC codes, and quasi-cyclic LDPC codes. The simulation results have shown that it can highly improve the fault tolerance ability compared to the existing Gauss elimination process-based algorithms.

• 한국통신학회논문지
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• 제33권12C호
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• pp.1062-1067
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• 2008

ABBA codes, a class of quasi-orthognal space-time block codes (QoSTBC) proposed by Tirkkonen and others, allow full rate and a fast maximum likelihood (ML) decoding, but do not have full diversity. In this paper, a linear complex precoder is proposed for ABBA codes to achieve full rate and full diversity. Moreover, the same diversity produce as that of orthogonal space-time block code with linear complex precoder (OSTBC-LCP) is achieved. Meanwhile, the size of the linear complex precoder can be reduced by half without affecting performance, which means the same complexity of decoding as that of the conventional ABBA code is guaranteed.

• 방송공학회논문지
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• 제16권6호
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• pp.1026-1035
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• 2011

본 논문은 기존 블록 터보 부호의 SISO(Soft-input Soft-output) 기반 반복 복호 알고리즘의 일반화 및 활용에 대한 연구를 다루고 있다. R. M. Pyndiah는 AWGN 채널(Additive White Gaussian Noise Channel)에서 2차원 Linear Block Code(선형 블록 부호, LBC) 결합으로 구성된 Product 부호의 SISO 반복 복호 방식을 제안했으며, 이를 블록 터보 부호라 하였다. 블록 터보 부호의 SISO 복호방식은 SIHO(Soft-input Hard-output) 복호 방식인 Chase 알고리즘의 부호 판정을 기반으로 연판정 정보를 생성 후 전달하여 반복적인 복호를 수행한다. 블록 터보 부호는 AWGN 채널에서 높은 Code-rate(부호율)의 Product 부호에 대해 적은 SISO 복호 반복만으로도 샤논 한계에 근접하는 우수한 성능을 보여준다. 본 논문에서는 BPSK(Binary Phase Shift Keying) 변조와 AWGN 채널 전송을 가정한 기존 블록 터보 부호 복호 알고리즘을 채널 출력의 LLR(Log-likelihood Ratio)에 기반한 알고리즘으로 일반화하고, LDPC(Low-density Parity Check) 부호와 블록 터보 부호의 직렬 결합 구조에서 일반화된 알고리즘 활용 예를 제시한다.

• 한국통신학회논문지
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• 제31권6C호
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• pp.575-581
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• 2006

본 논문에서는 Alamouti, Tarokh, Su와 Xia 등에 의해 도입된 직교 시공간 부호를 포함한 임의의 선형 직교 시공간 블록 부호에 대해, 준정지 레일리 페이딩 채널에서의 정확한 비트 오율 성능을 분석한다. 먼저 1차원 심볼 오류 함순(one-dimensional symbol error function, ODSEF)를 정의한다. 이것은 직교 시공간 블록 부호의 정확한 쌍 오류 확률(pairwise error probability)에 의하여 얻어진다. ODSEF와 Cho 와 Yoon의 QAM에 대한 비트 오율 표현을 이용하여, 직교 시공간 블록 부호에 대한 일반적인 표현을 구하고, 이를 이용하여, 선형 직교 시공간 블록 부호의 정확한 폐형의 비트 오율을 구한다.

• Journal of Communications and Networks
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• 제10권3호
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• pp.253-257
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• 2008

In this paper, the performance of generic orthogonal space-time block codes (OSTBCs) introduced by Alamouti [2], Tarokh [3], and Su and Xia [11] is analyzed. We first define one-dimensional component symbol error function (ODSEF) from the exact expression of the pairwise error probability of an OSTBC. Utilizing the ODSEF and the bit error probability (BEP) expression for quadrature amplitude modulation (QAM) introduced by Cho and Yoon [9], the exact closed-form expressions for the BEP of linear OSTBCs with QAM in quasi-static Rayleigh fading channel are derived. We also derive the exact closed-form of the BEP for some OSTBCs which have at least one message symbol transmitted with unequal power via all transmit antennas.

• 대한수학회보
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• 제60권3호
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• pp.829-844
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• 2023

In this paper, we present a new construction for self-dual codes that uses the concept of double bordered construction, group rings, and reverse circulant matrices. Using groups of orders 2, 3, 4, and 5, and by applying the construction over the binary field and the ring F₂ + uF₂, we obtain extremal binary self-dual codes of various lengths: 12, 16, 20, 24, 32, 40, and 48. In particular, we show the significance of this new construction by constructing the unique Extended Binary Golay Code [24, 12, 8] and the unique Extended Quadratic Residue [48, 24, 12] Type II linear block code. Moreover, we strengthen the existing relationship between units and non-units with the self-dual codes presented in [10] by limiting the conditions given in the corollary. Additionally, we establish a relationship between idempotent and self-dual codes, which is done for the first time in the literature.

• 전자공학회논문지A
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• 제30A권7호
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• pp.12-18
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• 1993

We have proposed a soft-decision decoding method for block codes. With careful examinations of the first hard-decision decoded results, The candidate codewords are efficiently searched for. Thus, we can reduce the decoding complexity (the number of hard-decision decodings) and lower the block error probability. Computer simulation results are presented for the (23,12) Golay code. They show that the decoding complexity is considerably reduced and the block error probability is close to that of the maximum likelihood decoder.

• 대한전자공학회논문지
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• 제27권2호
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• pp.9-15
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• 1990

本 論文에서는 線刑 2元 블럭 符號에 대한 軟判定 復號 알고리듬을 제안하였다. 이 알고리듬은 블록 誤謬 確率을 最小化하기 위한 것이다. 提案된 알고리듬을 기存의 다른 復號法과 비교하기 위하여(7,4) Hamming 符號와(23,12)Golay 符號에 대한 컴퓨터 시뮬레이션을 수행하였다. 그 결과, 提案된 알고리듬의 乎均 硬判定 復號 回數는 항상 2以下이며 信號對 雜音比가 충분히 클때 1에 접근하였다. 즉, 기存 다른 復號法에 비하여 復號의 複雜度가 減少되었음을 확인하였다.

• Journal of Communications and Networks
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• 제17권1호
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• pp.12-20
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• 2015

Convolutional codes which are terminated by direct truncation (DT) and zero tail termination provide unequal error protection. When DT terminated convolutional codes are used to encode short messages, they have interesting error protection properties. Such codes match the significance of the output bits of common quantizers and therefore lead to a low mean square error (MSE) when they are used to encode quantizer outputs which are transmitted via a noisy digital communication system. A code construction method that allows adapting the code to the channel is introduced, which is based on time-varying convolutional codes. We can show by simulations that DT terminated convolutional codes lead to a lower MSE than standard block codes for all channel conditions. Furthermore, we develop an MSE approximation which is based on an upper bound on the error probability per information bit. By means of this MSE approximation, we compare the convolutional codes to linear unequal error protection code construction methods from the literature for code dimensions which are relevant in analog to digital conversion systems. In numerous situations, the DT terminated convolutional codes have the lowest MSE among all codes.

• Journal of information and communication convergence engineering
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• 제20권1호
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• pp.1-7
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• 2022

Herein, a new space-time block coding technique is proposed for a MIMO 2 × 2 multiple-input multiple output (MIMO) system to minimize the bit error rate (BER) in Rayleigh fading channels with reduced decoding complexity using ZF and MMSE linear detection techniques. The main objective is to improve the service quality of wireless communication systems and optimize the number of antennas used in base stations and terminals. The idea is to exploit the correlation product technique between both information symbols to transmit per space-time block code and their own orthogonal Walsh-Hadamard sequences to ensure orthogonality between both symbol vectors and create a full-rate orthogonal STBC code. Using 16 quadrature amplitude modulation and the quasi-static Rayleigh channel model in the MATLAB environment, the simulation results show that the proposed space-time block code performs better than the Alamouti code in terms of BER performance in the 2 × 2 MIMO system for both cases of linear decoding ZF and MMSE.