• 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).

• 한국콘텐츠학회:학술대회논문집
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• 한국콘텐츠학회 2006년도 추계 종합학술대회 논문집
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• pp.647-651
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• 2006

본 논문에서는 국가 R&D관련 기관들의 데이터베이스에서 사용되고 있는 데이터 코드를 표준화하기 위해 R&D관련 4개 주요 기관들의 데이터베이스에서 사용되고 있는 코드를 비교분석하고, 코드 표준을 제정하기 위한 선행조사에 대하여 논한다. 조사결과 4대 주요 R&B관련 기관들의 DB에서 현재 코드로 관리하고 있는 개수는 340여개를 넘고 있었으며 이들 340여개 중에서 공통적이고 일반적인 것들이 150개로 서로 관련성이 있었다. 일반적이고 공통적인 150개 코드들에 대해 본 논문에서는 이들 150개 코드를 코드 의미에 따라 18개로 분류하고 코드 표준화를 위한 선행 조사를 행하였다.

• 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.

• Korean Journal of Mathematics
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• 제26권3호
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• pp.537-544
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• 2018

There is a standard construction of lifting cyclic codes over the prime finite field ${\mathbb{Z}}_p$ to the rings ${\mathbb{Z}}_{p^e}$ and to the ring of p-adic integers. We generalize this construction for arbitrary finite fields. This will naturally enable us to lift codes over finite fields ${\mathbb{F}}_{p^r}$ to codes over Galois rings GR($p^e$, r). We give concrete examples with all of the lifts.

• 대한수학회보
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• 제43권2호
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• pp.293-297
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• 2006

Using the concept of codes on ordered sets introduced by Brualdi, Graves and Lawrence, we consider perfect codes on the ordinal sum of two ordered sets, the standard ordered sets and the disjoint sum of two chains.

• ETRI Journal
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• 제45권3호
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• pp.404-417
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• 2023

This paper proposed a novel method for constructing quasi-cyclic low-density parity-check (QC-LDPC) codes of medium to high code rates that can be applied in cloud data storage systems, requiring better error correction capabilities. The novelty of this method lies in the construction of sparse base matrices, using a girth greater than 4 that can then be expanded with a lift factor to produce high code rate QC-LDPC codes. Investigations revealed that the proposed large-sized QC-LDPC codes with high code rates displayed low encoding complexities and provided a low bit error rate (BER) of 10^-10 at 3.5 dB E_b/N₀ than conventional LDPC codes, which showed a BER of 10^-7 at 3 dB E_b/N₀. Subsequently, implementation of the proposed QC-LDPC code in a softwaredefined radio, using the NI USRP 2920 hardware platform, was conducted. As a result, a BER of 10^-6 at 4.2 dB E_b/N₀ was achieved. Then, the performance of the proposed codes based on their encoding-decoding speeds and storage overhead was investigated when applied to a cloud data storage (GCP). Our results revealed that the proposed codes required much less time for encoding and decoding (of data files having a 10 MB size) and produced less storage overhead than the conventional LDPC and Reed-Solomon codes.

• 한국전자파학회논문지
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• 제15권1호
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• pp.81-88
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• 2004

3GPP 표준의 오류 정정 부호 기법 중의 하나로 채택된 turbo 부호는 그 성능이 Shannon이 제시하는 이론적 한계 값에 근사하기 때문에 많은 관심을 받고 있다. 그러나 계산상의 복잡함과 많은 메모리를 요구한다는 단점이 있고 이를 보완할 수 있는 Log-MAP, Max-Log-MAP, SOVA, sliding window 알고리즘 등이 제안되었다. 본 논문에서는 turbo복호 알고리즘을 부동 소수점 연산과 고정 소수점 연산을 이용하여 구현하였을 때 성능을 해석하였다. 그리고 Log-MAP 알고리즘의 성능에 근사하는 효율적인 고정 소수점 구현 방법을 제안하였다. 이 방법을 Log-MAP과 sliding window 알고리즘에 적용하여 성능을 분석하였다.

• Journal of Hydrospace Technology
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• 제2권1호
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• pp.55-64
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• 1996

Herein a review is made on the validation problem of numerical codes applied to floating offshore structures. Since the dynamic behaviour of offshore floating structures in water waves is in general complex and nonlinear, a numerical approach seems to be promising. However, numerical codes are likely involved with uncertainties and they at the present status show apparent scatterness in typical bechmark tests, particularly in second-order wave forces. Convergence test is the minimum requirement for the validation of numerical codes. Some other practical check points are introduced to clarify the potential error sources. It is concluded that a standard procedure for validation must be urgently established sothat numerical methods can safely be used as a rational design tool.

• 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 Communications and Networks
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• 제5권4호
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• pp.374-385
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• 2003

The growing interest towards ultra-wideband (UWB) communications stems from its unique features such as baseband operation, ample multipath diversity, and the potential of enhanced user capacity. But since UWB has to overlay existing narrowband systems, multiple access has to be achieved in the presence of narrowband interference (NBI). However, existing baseband spreading codes for UWB multiple access are not flexible in handling NBI. In this paper, we introduce two novel spreading codes that not only enable baseband UWB multiple access, but also facilitate flexible NBI cancellation. We construct our codes using a single carrier or multiple carriers (SC or MC), which can be implemented with standard discrete-cosine transform (DCT) circuits. With our SC/MC codes, NBI can be avoided by simply nulling undesired digital carriers. Being digital, these SC/MC codes give rise to multiband UWB systems, without invoking analog carriers. In addition, our SC/MC codes enable full multipath diversity, and maximum coding gains. Equally attractive is their capability to reduce the number of interfering users, with simple matched filter operations. Comprehensive simulations are also carried out to corroborate our analysis.