• Journal of Communications and Networks
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• v.10 no.1
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.2A
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• pp.138-143
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• 2006

We present upper bounds for the maximum-likelihood decoding performance of particular LDPC codes and turbo-like codes with particular interleavers. Previous research developed upper bounds for LDPC codes and turbo-like codes using ensemble codes or the uniformly interleaved assumption, which bound the performance averaged over all ensemble codes or all interleavers. Proposed upper bounds are based on the simple bound and estimated weight distributions including the exact several smallest distance terms because if either estimated weight distributions on their own or the exact several smallest distance terms only are used, an accurate bound can not be obtained.

• Journal of Advanced Marine Engineering and Technology
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• v.33 no.5
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• pp.738-745
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• 2009

Underwater acoustic communication has multipath error because of reflection by sea-level and sea-bottom. The multipath of underwater channel causes receive signal to make error floor. In this paper, we propose the underwater communication system using various channel coding schemes such as RS coding, convolutional code, turbo code and concatenated code for overcoming the multipath effect in underwater channel. As shown in simulation results, characteristic of multipath error is similar to that of random error. So interleaver has not effect on error correcting. For correcting of error floor by multipath, it is necessary to use strong channel codes like turbo code. Turbo code is one of the iterative codes. And the performance of concatenated codes including RS code has better performance than using singular channel codes.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.2
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• pp.157-162
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• 2016

The performance of turbo-like codes highly depends on their frame size and thus, the bit error rate performance of turbo-like codes can be improved by increasing the frame size. Unfortunately, increasing the frame size of channel codes induces some drawbacks such as the increase of not only encoding and decoding complexity but also transmission and decoding latencies. On the other hand, a faster than Nyquist (FTN) transmission causes intentional inter-symbol interference (ISI) and thus, induces some correlation among the transmission symbols. In this paper, we propose an FTN transmission with multiple channel codes. By exploiting the correlation among the modulated symbols, multiple code frames can be regarded as a code frame with a lager frame size. Due to the inherent parallel encoding scheme of proposed scheme, parallel decoding can be easily implemented.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.8A
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• pp.1254-1264
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• 2000

In this paper, we propose a new turbo interleaver and an efficient iteration control method with low complexity for turbo decoding. Turbo codes has better performance as the number of iteration and the interleaver size increases. However, as the interleaver size is increased, it require much delay and computation for decoding. Thus we propose a new efficient turbo magic interleaver using the Magic square matrix. Simulation results show that the proposed interleaver realizes a good performance like GF, Mother interleaver proposed to IMT-2000. And as the decoding approaches the performance limit, any further iteration results in very little improvement. Therefore, we propose an efficient algorithm of decoding that can reduce the delay and computation. Just like the conventional stop criterion, it effectively stop the iteration process with very little performance degradation.

• ETRI Journal
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• v.31 no.5
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• pp.585-592
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• 2009

This paper presents a method for decoding high minimal distance ($d_{min}$) short codes, termed Cortex codes. These codes are systematic block codes of rate 1/2 and can have higher$d_{min}$ than turbo codes. Despite this characteristic, these codes have been impossible to decode with good performance because, to reach high $d_{min}$, several encoding stages are connected through interleavers. This generates a large number of hidden variables and increases the complexity of the scheduling and initialization. However, the structure of the encoder is well suited for analog decoding. A proof-of-concept Cortex decoder for the (8, 4, 4) Hamming code is implemented in subthreshold 0.25-${\mu}m$ CMOS. It outperforms an equivalent LDPC-like decoder by 1 dB at BER=$10^{-5}$ and is 44 percent smaller and consumes 28 percent less energy per decoded bit.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.39 no.4
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• pp.165-172
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• 2002

In the next generation mobile communications, powerful channel coding is essential in order to obtain high quality multimedia services. Turbo code can achieve good error performance by iterative decoding, but more iterations result in additional computational complexity and delay. Thus, a method to reduce the number of iterations without additional performance degradation is needed. Turbo code with CRC is known to be the most efficient method to reduce the number of iterations. In this scheme, the performance may be degraded by the edge-effect like the conventional turbo code without CRC. In this paper, a method to eliminate the edge-effect is proposed by adopting D-parameter to the conventional s-random interleaver. As results of simulation, the edge-effect of the turbo code with CRC is shown to be successfully eliminated by using the new interleaver designed with D-parameter.

• The Journal of the Acoustical Society of Korea
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• v.27 no.6
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• pp.286-295
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• 2008

Underwater acoustic communication has multi path error because of reflection by sea-level and sea-bottom. The multipath of underwater channel causes signal distortion and error floor. In this paper, we consider the use of various channel coding schemes such as RS code, convolutional code, cross-layer code and LDPC code in order to compensate the multipath effect in underwater channel. As shown in simulation results, characteristic of multipath error is similar to that of random error, so interleaver has little effect for error correcting. For correcting of error floor by multipath error, it is necessary strong channel codes like LDPC code that is similar to Shannon's limit. And the performance of concatenated codes including RS codes has better performance than using singular channel codes.

• Journal of information and communication convergence engineering
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• v.8 no.6
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• pp.655-659
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• 2010

In the conventional PNC scheme, the relay node requires simultaneous transmission of two source nodes with strict power control and carrier-phase matching between two received symbols. However, this pre-equalization process at source nodes is not practical in fading channels. In this letter, we propose a novel physical-layer network coding (PNC) scheme with log-likelihood ratio (LLR) conversion for fading channels, which utilizes not pre-equalizer at transmitters (source nodes) but joint detector at receiver (relay node). The proposed PNC requires only channel side information at the receiver (CSIR), which is far more practical assumption in fading channels. In addition, the proposed PNC scheme can use the conventional modulation scheme like M-QAM regardless of modulation order, while the conventional PNC scheme requires reconfiguration of modulation scheme at the source nodes for detection of the received signal at relay node. We consider the combination of the proposed PNC and channel coding, and find that the proposed PNC scheme is easily combined the linear channel codes such as turbo codes, LDPC, and convolutional codes.

• Journal of Communications and Networks
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• v.17 no.4
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• pp.339-345
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• 2015

In this paper, we present an iterative reliability-based modified majority-logic decoding algorithm for two classes of structured low-density parity-check codes. Different from the conventional modified one-step majority-logic decoding algorithms, we design a turbo-like iterative strategy to recover the performance degradation caused by the simply flipping operation. The main computational loads of the presented algorithm include only binary logic and integer operations, resulting in low decoding complexity. Furthermore, by introducing the iterative set, a very small proportion (less than 6%) of variable nodes are involved in the reliability updating process, which can further reduce the computational complexity. Simulation results show that, combined with the factor correction technique and a well-designed non-uniform quantization scheme, the presented algorithm can achieve a significant performance improvement and a fast decoding speed, even with very small quantization levels (3-4 bits resolution). The presented algorithm provides a candidate for trade-offs between performance and complexity.