• Journal of Communications and Networks
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• 제10권1호
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• pp.5-9
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• 2008

Researchers have investigated many upper bound techniques applicable to error probabilities on the maximum likelihood (ML) decoding performance of turbo-like codes and low density parity check (LDPC) codes in recent years for a long codeword block size. This is because it is trivial for a short codeword block size. Previous research efforts, such as the simple bound technique [20] recently proposed, developed upper bounds for LDPC codes and turbo-like codes using ensemble codes or the uniformly interleaved assumption. This assumption bounds the performance averaged over all ensemble codes or all interleavers. Another previous research effort [21] obtained the upper bound of turbo-like code with a particular interleaver using a truncated union bound which requires information of the minimum Hamming distance and the number of codewords with the minimum Hamming distance. However, it gives the reliable bound only in the region of the error floor where the minimum Hamming distance is dominant, i.e., in the region of high signal-to-noise ratios. Therefore, currently an upper bound on ML decoding performance for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix cannot be calculated because of heavy complexity so that only average bounds for ensemble codes can be obtained using a uniform interleaver assumption. In this paper, we propose a new bound technique on ML decoding performance for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix using ML estimated weight distributions and we also show that the practical iterative decoding performance is approximately suboptimal in ML sense because the simulation performance of iterative decoding is worse than the proposed upper bound and no wonder, even worse than ML decoding performance. In order to show this point, we compare the simulation results with the proposed upper bound and previous bounds. The proposed bound technique is based on the simple bound with an approximate weight distribution including several exact smallest distance terms, not with the ensemble distribution or the uniform interleaver assumption. This technique also shows a tighter upper bound than any other previous bound techniques for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix.

• 대한수학회지
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• 제48권3호
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• pp.475-486
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• 2011

The paper deals with repeated low-density burst error detecting codes with a specied weight or less. Linear codes capable of detecting such errors have been studied. Further codes capable of correcting and simultaneously detecting such errors have also been dealt with. The paper obtains lower and upper bounds on the number of parity-check digits required for such codes. An example of such a code has also been provided.

• 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.

• Journal of Communications and Networks
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• 제17권4호
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• pp.351-361
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• 2015

In this paper, a new decoding scheme is proposed to improve the error correcting performance of low-density parity-check (LDPC) codes in high signal-to-noise ratio (SNR) region by using post-processing. It behaves as follows: First, a conventional LDPC decoding is applied to received LDPC codewords one by one. Then, we count the number of word errors in a predetermined number of decoded codewords. If there is no word error, nothing needs to be done and we can move to the next group of codewords with no delay. Otherwise, we perform a proper post-processing which produces a new soft-valued codeword (this will be fully explained in the main body of this paper) and then apply the conventional LDPC decoding to it again to recover the unsuccessfully decoded codewords. For the proposed decoding scheme, we adopt a simple product code structure which contains LDPC codes and simple algebraic codes as its horizontal and vertical codes, respectively. The decoding capability of the proposed decoding scheme is defined and analyzed using the parity-check matrices of vertical codes and, especially, the combined-decodability is derived for the case of single parity-check (SPC) codes and Hamming codes used as vertical codes. It is also shown that the proposed decoding scheme achieves much better error correcting capability in high SNR region with little additional decoding complexity, compared with the conventional LDPC decoding scheme.

• Journal of Communications and Networks
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• 제16권3호
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• pp.249-257
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• 2014

This paper presents methods to the construction of regular and irregular low-density parity-check (LDPC) codes based on Euclidean geometries over the Galois field. Codes constructed by these methods have quasi-cyclic (QC) structure and large girth. By decomposing hyperplanes in Euclidean geometry, the proposed irregular LDPC codes have flexible column/row weights. Therefore, the degree distributions of proposed irregular LDPC codes can be optimized by technologies like the curve fitting in the extrinsic information transfer (EXIT) charts. Simulation results show that the proposed codes perform very well with an iterative decoding over the AWGN channel.

• 한국통신학회논문지
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• 제41권12호
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• pp.1745-1747
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• 2016

본 논문에서 다양한 블록 크기를 가지는 완전 차집합군을 이용하여 불규칙 준순환 패리티 체크 부호를 생성하는 방법을 제안한다. 제안하는 부호는 기존의 설계방법들에 비해 부호율, 부호 길이, 차수 분포 측면에서 다양한 값들을 가질 수 있다는 장점을 보인다. 또한 랜덤한 방법으로 설계하기 힘든 매우 짧은 길이의 부호를 체계적으로 설계할 수 있다. 모의실험을 통해 제안하는 부호의 오류 정정 성능을 검증한다.

• 방송공학회논문지
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• 제25권1호
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• pp.36-47
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• 2020

향상된 신뢰-전파 기반 알고리즘인 정규화 최소-합 알고리즘 혹은 오프셋 최소-합 알고리즘은 낮은 연산복잡도와 높은 복호 성능을 보여 LDPC(Low-Density Parity-Check) 부호의 복호에 널리 이용되고 있다. 그러나, 이 알고리즘들은 적절한 정규화 계수와 오프셋 계수가 이용되어야만 높은 복호 성능을 갖는다. 최근 제안된 CMD(Check Node Message Distribution) 차트와 최소자승법을 이용하여 정규화 계수를 찾는 방법은 기존의 계수 도출 방법보다 계산량이 적을 뿐 아니라 각 반복 복호마다 최적의 정규화 계수를 도출할 수 있기 때문에 복호 성능을 높일 수 있다. 본 논문에서는 이 방법을 응용하여 정규화와 오프셋이 조합된 최소-합 알고리즘의 보정 계수 조합의 도출을 위한 알고리즘을 제안하고자 한다. 차세대 방송 통신 표준인 ATSC 3.0용 LDPC 부호의 컴퓨터 모의실험은 제안한 알고리즘을 통해 도출된 보정 계수 조합을 사용하였을 때 타 복호 알고리즘보다 월등히 높은 복호 성능을 가지는 것을 보인다.

• Journal of Communications and Networks
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• 제14권4호
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• pp.429-433
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• 2012

In this paper, we consider nonbinary quasi-cyclic low-density parity-check (QC-LDPC) codes and propose a method to design multiple rate codes with either fixed information bit length or block bit length, tailored to different scenarios in wireless applications. We show that the proposed codes achieve good performance over a broad range of code rates.

• Journal of Communications and Networks
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• 제15권2호
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• pp.217-221
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• 2013

Quantum low-density parity-check (LDPC) codes based on the Calderbank-Shor-Steane construction have low encoding and decoding complexity. The sum-product algorithm(SPA) can be used to decode quantum LDPC codes; however, the decoding performance may be significantly decreased by the many four-cycles required by this type of quantum codes. All four-cycles can be eliminated using the entanglement-assisted formalism with maximally entangled states (ebits). The proposed entanglement-assisted quantum error-correcting code based on Euclidean geometry outperform differently structured quantum codes. However, the large number of ebits required to construct the entanglement-assisted formalism is a substantial obstacle to practical application. In this paper, we propose a novel class of entanglement-assisted quantum LDPC codes constructed using classical Euclidean geometry LDPC codes. Notably, the new codes require one copy of the ebit. Furthermore, we propose a construction scheme for a corresponding zigzag matrix and show that the algebraic structure of the codes could easily be expanded. A large class of quantum codes with various code lengths and code rates can be constructed. Our methods significantly improve the possibility of practical implementation of quantum error-correcting codes. Simulation results show that the entanglement-assisted quantum LDPC codes described in this study perform very well over a depolarizing channel with iterative decoding based on the SPA and that these codes outperform other quantum codes based on Euclidean geometries.

• IEIE Transactions on Smart Processing and Computing
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• 제6권3호
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• pp.210-219
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• 2017

This paper proposes a modified min-max algorithm (MMMA) for nonbinary quasi-cyclic low-density parity-check (NB-QC-LDPC) codes and an efficient parallel block-layered decoder architecture corresponding to the algorithm on a graphics processing unit (GPU) platform. The algorithm removes multiplications over the Galois field (GF) in the merger step to reduce decoding latency without any performance loss. The decoding implementation on a GPU for NB-QC-LDPC codes achieves improvements in both flexibility and scalability. To perform the decoding on the GPU, data and memory structures suitable for parallel computing are designed. The implementation results for NB-QC-LDPC codes over GF(32) and GF(64) demonstrate that the parallel block-layered decoding on a GPU accelerates the decoding process to provide a faster decoding runtime, and obtains a higher coding gain under a low $10^{-10}$ bit error rate and low $10^{-7}$ frame error rate, compared to existing methods.