• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.2C
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• pp.219-228
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• 2010

In this paper, performance of RS (Reed-Solomon), turbo and LDPC (low density parity check) code in the binary symmetric erasure channel is investigated. When the average erasure length is reduced, the frequency of short erasures is increased. The RS code shows serious performance degradation in such an environment since decoding is carried out symbol-by-symbol. As the erasure length is increased, however, the RS code shows much improved en-or performance. On the other hand, the message and corresponding parity symbols of the turbo code can be erased at the same time for the long erasures. Accordingly, iterative decoding of the turbo code can not improve error performance any more for such a long erasure. The LDPC code shows little difference in error performance with respect to the variation of the average erasure length due to the virtual interleaving effect. As a result, the LDPC code has much better erasure decoding performance than the RS and turbo code.

• ETRI Journal
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• v.31 no.5
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• pp.518-524
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• 2009

Single parity check (SPC) product codes are simple yet powerful codes that are used to correct errors and/or recover erasures. The focus of this paper is to evaluate the performance of such codes under erasure scenarios and to develop a closed-form tight upper bound for the post-decoding erasure rate. Closed-form exact expressions are derived for up to seven erasures. Previously published closed-form bounds assumed that all unrecoverable patterns should contain four erasures in a square. Additional non-square patterns are accounted for in the proposed expressions. The derived expressions are verified using exhaustive search. Eight or more erasures are accounted for by using a bound. The developed expressions improve the evaluation of the recoverability of SPC product codes without the need for simulation or search algorithms, whether exhaustive or novel.

• Journal of the Institute of Electronics and Information Engineers
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• v.49 no.12
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• pp.27-35
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• 2012

In this paper, we look into a Jong Nang Channel which is the origin of digital communications and has been used in Jeju Island since AD 1234. It is one kind of communication ways which informs people of whether a house owner is in one's house or not using its own protocol. It is comprised of three timber and two stone pillars whose one side has three holes respectively. In this paper, we analyze the Jong-Nang Channel both in the light of logic and bit error probability. In addition, we compare it with a conventional binary erasure channel when some errors occur over them respectively. We also show that a capacity of NOR channel approaches Shannon limit.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.15 no.5
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• pp.91-103
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• 2015

This paper presents "The 3-User NOR switching channel based on interference decoding with receiver cooperation" in succession to "Jeju Jong Nang channel code I, II". The Jeju Jong Nang code is considered as one of the earliest human binary coded communication (HBCC) in the world with a definite "1" or "0" binary symbolic analysis of switching circuits. In this paper, we introduce a practical example of interference decoding with receiver cooperation based on the three user Jong Nang NOR switching channel. The proposed system models are the three user Jong Nang (TUJN) NOR logic switching on-off, three-user injective deterministic NOR switching channel and Gaussian interference channel (GIC) with receiver cooperation. Therefore, this model is well matched to Shannon binary symmetric and erasure channel capacity. We show the applications of three-user Gaussian interference decoding to obtain deterministic channels which means each receiver cooperation helps to adjacent others in order to increase degree of freedom. Thus, the optimal sum rate of interference mitigation through adjacent receiver cooperation achieves 7 bits.

• Journal of Communications and Networks
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• v.15 no.4
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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.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.8
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• pp.3-14
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• 2013

We demonstrate a fashion of quantum channel combining and splitting, called polar quantum channel coding, to generate a quantum bit (qubit) sequence that achieves the symmetric capacity for any given binary input discrete quantum channels. The present capacity is achievable subject to input of arbitrary qubits with equal probability. The polarizing quantum channels can be well-conditioned for quantum error-correction coding, which transmits partially quantum data through some channels at rate one with the symmetric capacity near one but at rate zero through others.