• ETRI Journal
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• 제32권6호
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• pp.972-975
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• 2010

In this letter, we consider the lossy coding of a non-uniform binary source based on GF(q)-quantized low-density generator matrix (LDGM) codes with check degree $d_c$=2. By quantizing the GF(q) LDGM codeword, a non-uniform binary codeword can be obtained, which is suitable for direct quantization of the non-uniform binary source. Encoding is performed by reinforced belief propagation, a variant of belief propagation. Simulation results show that the performance of our method is quite close to the theoretic rate-distortion bounds. For example, when the GF(16)-LDGM code with a rate of 0.4 and block-length of 1,500 is used to compress the non-uniform binary source with probability of 1 being 0.23, the distortion is 0.091, which is very close to the optimal theoretical value of 0.074.

• Journal of Communications and Networks
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• 제12권5호
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• pp.406-410
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• 2010

This paper presents an approach to the construction of non-binary quasi-cyclic (QC) low-density parity-check (LDPC) codes based on multiplicative groups over one Galois field GF(q) and Euclidean geometries over another Galois field GF($2^S$). Codes of this class are shown to be regular with girth $6{\leq}g{\leq}18$ and have low densities. Finally, simulation results show that the proposed codes perform very wel with the iterative decoding.

• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제15권2호
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• pp.485-499
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• 2021

Although non-binary low-density parity-check (NB-LDPC) codes have better error-correction capability than that of binary LDPC codes, their decoding complexity is significantly higher. Therefore, it is crucial to reduce the decoding complexity of NB-LDPC while maintaining their error-correction capability to adopt them for various applications. The extended min-sum (EMS) algorithm is widely used for decoding NB-LDPC codes, and it reduces the complexity of check node (CN) operations via message truncation. Herein, we propose a low-cost CN processing method to reduce the complexity of CN operations, which take most of the decoding time. Unlike existing studies on low complexity CN operations, the proposed method employs quick selection algorithm, thereby reducing the hardware complexity and CN operation time. The experimental results show that the proposed selection-based CN operation is more than three times faster and achieves better error-correction performance than the conventional EMS algorithm.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제9권7호
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• pp.2599-2613
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• 2015

Multi-index hashing (MIH) is the state-of-the-art method for indexing binary codes, as it di-vides long codes into substrings and builds multiple hash tables. However, MIH is based on the dataset codes uniform distribution assumption, and will lose efficiency in dealing with non-uniformly distributed codes. Besides, there are lots of results sharing the same Hamming distance to a query, which makes the distance measure ambiguous. In this paper, we propose a data-oriented multi-index hashing method (DOMIH). We first compute the covariance ma-trix of bits and learn adaptive projection vector for each binary substring. Instead of using substrings as direct indices into hash tables, we project them with corresponding projection vectors to generate new indices. With adaptive projection, the indices in each hash table are near uniformly distributed. Then with covariance matrix, we propose a ranking method for the binary codes. By assigning different bit-level weights to different bits, the returned bina-ry codes are ranked at a finer-grained binary code level. Experiments conducted on reference large scale datasets show that compared to MIH the time performance of DOMIH can be improved by 36.9%-87.4%, and the search accuracy can be improved by 22.2%. To pinpoint the potential of DOMIH, we further use near-duplicate image retrieval as examples to show the applications and the good performance of our method.

• 한국방송∙미디어공학회:학술대회논문집
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• 한국방송공학회 2010년도 추계학술대회
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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.

• Journal of Communications and Networks
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• 제17권4호
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• pp.328-338
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• 2015

Three areas of ongoing research in channel coding are surveyed, and recent developments are presented in each area: Spatially coupled low-density parity-check (LDPC) codes, nonbinary LDPC codes, and polar coding.

• 한국통신학회논문지
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• 제39A권3호
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• pp.127-139
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• 2014

멀티 레벨 낸드 플래시 메모리는 한 셀에 2 비트 이상의 정보를 저장하는 구조이고, 비트 위치별 채널 LLR의 밀도 함수 l-밀도가 비대칭 특성을 가지고 있다. 이런 특성은 이진 무기억 대칭 채널 조건에서 설계된 오류 정정부호의 성능이 제대로 발휘되지 못하게 할 뿐만 아니라, 멀티 레벨 낸드 플래시 메모리용 연판정 복호를 수행하는 이진 오류 정정 부호의 설계도 어렵게 한다. 본 논문에서 밀도 미러링과 EM 알고리즘을 이용하여 오류 정정 부호 설계를 위한 차선책을 소개한다. 밀도 미러링은 EM 알고리즘을 적용하기 전에 0 부호어를 전송한 경우로 가정할 수 있도록 하기 위해서 채널 LLR을 처리하는 과정이고, 이후 채널 LLR l-밀도를 EM 알고리즘을 적용하여 K개의 성분으로 이루어진 대칭 가우시안 혼합 밀도로 근사화하는 방법을 소개한다.

• 대한수학회보
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• 제54권4호
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• pp.1111-1122
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• 2017

In this work, we consider constacyclic and cyclic self-dual codes over the rings $R_k$. We start with theoretical existence results for constacyclic and cyclic self-dual codes of any length over $R_k$ and then construct cyclic self-dual codes over $R_1={\mathbb{F}}_2+u{\mathbb{F}}_2$ of even lengths from lifts of binary cyclic self-dual codes. We classify all free cyclic self-dual codes over $R_1$ of even lengths for which non-trivial such codes exist. In particular we demonstrate that our constructions provide a counter example to a claim made by Batoul et al. in [1] and we explain why their claim fails.

• 대한수학회보
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• 제55권1호
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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.