• 한국통신학회논문지
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• 제39A권10호
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• pp.585-592
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• 2014

It is well known that serial belief propagation (BP) decoding for low-density parity-check (LDPC) codes achieves faster convergence without any increase of decoding complexity per iteration and bit error rate (BER) performance loss than standard parallel BP (PBP) decoding. Serial BP (SBP) decoding, such as horizontal SBP (H-SBP) decoding or vertical SBP (V-SBP) decoding, updates check nodes or variable nodes faster than standard PBP decoding within a single iteration. In this paper, we propose combined horizontal-vertical SBP (CHV-SBP) decoding. By the same reasoning, CHV-SBP decoding updates check nodes or variable nodes faster than SBP decoding within a serialized step in an iteration. CHV-SBP decoding achieves faster convergence than H-SBP or V-SBP decoding. We compare these decoding schemes in details. We also show in simulations that the convergence rate, in iterations, for CHV-SBP decoding is about $\frac{1}{6}$ of that for standard PBP decoding, while the convergence rate for SBP decoding is about $\frac{1}{2}$ of that for standard PBP decoding. In simulations, we use recently proposed generalized LDPC (GLDPC) codes with binary cyclic codes (BCC).

• 한국통신학회논문지
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• 제33권2C호
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• pp.173-177
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• 2008

본 논문에서, 우리는 다수의 짧은 주기들을 추가함으서 LDPC 부호의 성능을 향상시킨다. 짧은 주기, 특히 길이가 4인 주기는 만약 표준 BP 복호가 쓰인다면 LDPC 부호의 성능을 저하시킨다. 그래서 현재의 연구들은 성능 높은 LDPC 부호를 설계하기 위하여 길이가 4인 주기들을 없애는데 초점을 맞추고 있다. 우리는 만약 수정된 BP 복호를 사용하면 다수의 길이가 4인 주기들은 LDPC 부호의 성능을 향상 시키는 것을 발견했다. 본 논문에서는 다수의 짧은 주기들을 가진 LDPC 부호를 위한 수정된 BP 복호 알고리즘이 소개되고 또한 다수의 짧은 주기들을 가지는 LDPC 부호의 수정된 BP 복호성능이 짧은 주기를 가지지 않는 LDPC 부호의 표준 BP 복호 성능보다 우수함을 보였다.

• 한국통신학회논문지
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• 제34권11C호
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• pp.1025-1028
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• 2009

본 논문에서는 기존의 단순 한계와 Maximum Likelihood (ML) 추정 입력 출력 무게 분포를 사용하여 몇 개의 불규칙한 LDPC 부호의 ML 복호에 대한 성능의 상향 한계를 구하고 부호의 길이가 길어지면 Belief-Propagation (BP) 복호의 성능이 ML 복호 성능에 단순하게 근접해 간다는 일반적인 견해와는 상반되게 정점 성능 감쇠(Peak Degradation)에 다다르기 이전에는 부호의 길이가 길어지면 오히려 BP 복호의 성능이 ML 복호 성능으로부터 성능 감쇠 폭이 증가하고 정점 성능 감쇠를 지난 후에 일반적인 견해가 적용되는 것을 보인다.

• 한국통신학회논문지
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• 제35권7C호
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• pp.594-597
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• 2010

This paper estimates belief-propagation (BP) decoding performance of moderate-length irregular low-density parity-check (LDPC) codes with sphere bounds. We note that for moderate-length($10^3{\leq}N{\leq}4\times10^3$) irregular LDPC codes, BP decoding performance, which is much worse than maximum likelihood (ML) decoding performance, is well matched with one of loose upper bounds, i.e., sphere bounds. We introduce the sphere bounding technique for particular codes, not average bounds. The sphere bounding estimation technique is validated by simulation results. It is also shown that sphere bounds and BP decoding performance of irregular LDPC codes are very close at bit-error-rates (BERs) $P_b$ of practical importance($10^{-5}{\leq}P_b{\leq}10^{-4}$).

• ETRI Journal
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• 제34권5호
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• pp.719-726
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• 2012

Messages are generally selected with the same probability in the encoding scheme of rateless codes for equal error protection. In addition, a belief propagation (BP) decoding scheme is generally used because of the low computational complexity. However, the probability of recovering a new message by BP decoding is reduced if both the recovered and unrecovered messages are selected uniformly. Thus, more codeword symbols than expected are required for the perfect recovery of message symbols. Therefore, a new encoding scheme with a nonuniform selection of messages is proposed in this paper. In addition, a BP-Gaussian elimination hybrid decoding scheme that complements the drawback of the BP decoding scheme is proposed. The performances of the proposed schemes are analyzed and compared with those of the conventional schemes.

• 한국정보전자통신기술학회논문지
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• 제7권4호
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• pp.223-228
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• 2014

LT 부호에 대해 BP 복호 알고리즘은 가장 빠른 복호 방법 중 하나로 알려져 있다. 그러나 BP 알고리즘은 대부분의 LT 부호를 복호하는데 있어서 많은 오버헤드를 요구하며 특히 짧은 길이의 LT 부호에 대해서는 과다한 오버헤드가 소요된다. 본 논문에서는 오버헤드를 줄이기 위해 1-차수의 패킷을 탐색할 수 있는 방법을 제시하고 이를 이용한 개선된 BP 복호 알고리즘을 제안하였다. 제안된 복호 알고리즘은 기존의 BP 알고리즘에 비해 같은 복호 복잡도를 유지하면서도 더 적은 오버헤드를 가짐을 알 수 있었다.

• Journal of Communications and Networks
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• 제15권4호
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• pp.411-421
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• 2013

Digital fountain codes are record-breaking codes for erasure channels. They have many potential applications in both wired and wireless communications. Most existing digital fountain codes operate over binary fields using an iterative belief-propagation (BP) decoding algorithm. In this paper, we propose a new iterative decoding algorithm for both binary and nonbinary fields. The basic form of our proposed algorithm considers both degree-1 and degree-2 check nodes (instead of only degree-1 check nodes as in the original BP decoding scheme), and has linear complexity. Extensive simulation demonstrates that it outperforms the original BP decoding scheme, especially for a small number of source packets. The enhanced form of the proposed algorithm combines the basic form of the algorithm and a guess-based algorithm to further improve the decoding performance. Simulation results demonstrate that it can provide better decoding performance than the guess-based algorithm with fewer guesses, and can achieve decoding performance close to that of the maximum likelihood decoder at a much lower decoding complexity. Last, we show that our nonbinary scheme has the potential to outperform the binary scheme when choosing suitable degree distributions, and furthermore it is insensitive to the size of the Galois field.

• 한국통신학회논문지
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• 제33권11C호
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• pp.880-882
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• 2008

This paper presents LDPC codes' upper bounds over the waterfall SNR region. The previous researches have focused on the average bound or ensemble bound over the whole SNR region and showed the performance differences for the fixed block size. In this paper, the particular LDPC codes' upper bounds for various block sizes are calculated over the waterfall SNR region and are compared with BP decoding performance. For different block sizes the performance degradation of BP decoding is shown.

• 전기학회논문지P
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• 제59권1호
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• pp.53-57
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• 2010

Low-density parity-check (LDPC) codes with belief-propagation (BP) algorithm achieve a remarkable performance close to the Shannon limit at reasonable decoding complexity. Conventionally, each iteration in decoding process contains two steps, the horizontal step and the vertical step. In this paper, an efficient implementation of the adaptive offset min-sum (AOMS) algorithm for decoding LDPC codes using the single-step method is proposed. Furthermore, the performances of the AOMS algorithm compared with belief-propagation (BP) algorithm are investigated. The algorithms using the single-step method reduce the implementation complexity, speed up the decoding process and have better efficiency in terms of memory requirements.

• ETRI Journal
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• 제26권5호
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• pp.432-436
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• 2004

In this paper, we propose the modified uniformly most powerful (UMP) belief-propagation (BP)-based decoding algorithm which utilizes multiplicative and additive factors to diminish the errors introduced by the approximation of the soft values given by a previously proposed UMP BP-based algorithm. This modified UMP BP-based algorithm shows better performance than that of the normalized UMP BP-based algorithm, i.e., it has an error performance closer to BP than that of the normalized UMP BP-based algorithm on the additive white Gaussian noise channel for low density parity check codes. Also, this algorithm has the same complexity in its implementation as the normalized UMP BP-based algorithm.