• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.6C
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• pp.337-342
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• 2011

In 2009, polar codes, proposed by Arikan, are theoretically proven codes to achieve capacity with acceptable encoding and decoding complexity. Currently, polar codes using channel polarization phenomenon are studied in security and data compression fields etc. In this paper, we consider the practical communication system and propose the construction method of polar codes with finite length and fixed code rate. Also, we show the outstanding performance and corresponding construction method of polar codes found by heuristic simulation.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38C no.1
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• pp.109-117
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• 2013

Polar codes are the first provable error correcting code achieving the symmetric channel capacity in a wide case of binary input discrete memoryless channel(BI-DMC). However, finite length polar codes have an error floor problem with successive-cancellation list(SCL) decoder. From previous works, we can solve this problem by concatenating CRC(Cyclic Redundancy Check) codes. In this paper we propose to make polar codes having extended-minimum distance from original polar codes without outer codes using correlation with generate matrix of polar codes and that of RM(Reed-Muller) codes. And we compare performance of proposed polar codes with that of polar codes concatenating CRC codes.

• Journal of the Institute of Electronics and Information Engineers
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• v.52 no.10
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• pp.3-10
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• 2015

Application of polar codes to rate-adaptive asymmetric Slepian-Wolf coding is considered. We propose a method of constructing polar codes which supports rate adaptivity. The proposed polar distributed source coding with successive cancellation list decoding performs closer to the Slepian-Wolf bound than the low density parity check accumulate (LDPCA) codes in the same framework.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.48 no.4
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• pp.24-36
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• 2011

In this paper, we verify the channel synthesis and decomposition of polar codes using successive cancellation decoding algorithm over binary discrete memoryless symmetric channel by modifying Arikan's algebraic formular on encoding and decoding of polar codes. In addition, we found that information bits are sent by efficiently consisting of polar codes with their size $2^n$ through polarizing matrix ${G_2}^{{\otimes}n}$ over binary discrete memoryless symmetric channel W. Expecially, if $N{\geq}2$, the complexity of Arikan's encoding and decoding for polar codes is O($Nlog_2N$). Furthermore, we found that polar codes are one of the solution to the challenging problems for the multipoint communication.

• Journal of IKEEE
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• v.23 no.4
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• pp.1288-1294
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• 2019

The channel-achieving property made the polar code show to advantage as an error-correcting code. However, sufficient error-correction performance shows the asymptotic property that is achieved when the length of the code is long. Therefore, efficient architecture is needed to realize the implementation of very-large-scale integration for the case of long input data. Although the most basic fully parallel encoder is intuitive and easy to implement, it is not suitable for long polar codes because of the high hardware complexity. Complementing this, a partially parallel encoder was proposed which has an excellent result in terms of hardware area. Nevertheless, this method has not been completely generalized and has the disadvantage that different architectures appear depending on the hardware designer. In this paper, we propose a hardware design scheme that applies the proposed systematic approach which is optimized for bit-dimension permutations. By applying this solution, it is possible to design a generalized partially parallel encoder for long polar codes with the same intuitive architecture as a fully parallel encoder.

• Information and Communications Magazine
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• v.29 no.8
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• pp.26-33
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• 2012

차세대 통신 시스템에서는 고속 데이터 전송을 위해 다수의 송신자와 수신자가 네트워크를 구성하여 정보를 주고 받는 다자간 협력 통신을 가정한다. 이러한 상황에 적합한 오류 정정 부호로 이미 탁월한 오류 정정 능력을 검증 받은 저밀도 패리티 체크 (low-density parity-check, LDPC)부호, 이진 입력 이산 비기억 (discrete memoryless) 채널에서 무한한 길이에 대하여 채널 용량 (channel capacity)을 달성하는 것으로 알려진 극 부호 (polar code), 아직은 많이 개발되지 않았지만 보다 높은 전송률을 달성할 수 있는 다중점 (multiple point) 채널에서의 새로운 부호 등이 거론될 수 있다. 본고에서는 이러한 차세대 통신 시스템을 위한 오류 정정 부호들에 대해서 기본 이론과 최근 연구 동향, 그리고 향후 연구 방향 등을 소개하도록 한다.

• Information and Communications Magazine
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• v.28 no.9
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• pp.84-95
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• 2011

2011년 IEEE 국제 정보 이론(ISIT) 심포지엄 (Symposium) 이 7월 31일부터 8월 5일까지 러시아 상트페테르부르크(St. Petersburg)에서 열렸다. 본 심포지엄에는 총 1,562편의 논문이 수락되어, 논문 수락율이 약 60%로 높지만, 최고 수준의 심포지엄으로, 1,500여명의 학자들이 참여했으며, 학문적으로 정보 이론의 핵심인 체비쇼프 다항식, 마코프 확률 연쇄, 콜모고로프 엔트로피, 페렐만의 푸앵카레 추측 증명 등, 학문의 원천 아이디어 발상에 대해 고찰하고, 최근 뜨거운 감자로 떠오른 극 부호(Po1ar code)를 간단히 소개했다. 또한, 우리 전통 문화 유산인 제주 정낭을 채널 부호의 관점에서 해석, 이에 따른 채널 용량을 구했고, 제주 정낭이 오늘날 중계망(Relay network)의 모태임을 증명했다.

• Journal of IKEEE
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• v.22 no.4
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• pp.1168-1174
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• 2018

For the initial state of NAND flash memories, error-free and single-error cases are dominant due to a good channel environment on memory cells. It is important to deal with such cases, which affects the overall system performance. However, the conventional schemes for polar codes equally decode the codes even for the error-free and single-error cases since they cannot classify and decode separately. In this paper, a new pre-processing scheme for polar codes is proposed so as to improve the overall decoding latency by decoding the frequent error-free and single-error cases. Before the ordinary decoding process, the proposed scheme first decodes the frequent error-free and single-error cases. According to the experimental results, the proposed pre-processing scheme decreases the average decoding latency by 64% compared to the conventional scheme for (1024, 512) polar codes.

• Proceedings of the IEEK Conference
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• 2007.07a
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• pp.71-72
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• 2007

대역 제한된 DS/SS 시스템의 상관 함수는 최고 값이 나타나는 시점과 함께 이른 또는 늦은 상관시간 옵셋 영역에서 극소 또는 극대로 나타나는 시점을 특징점으로 갖는다. 이 가운데 이른 상관시간옵셋 영역의 상관 함수는 다중경로 신호에 의해 덜 왜곡되기 때문에 이 영역의 상관 함수를 이용해 부호 동기를 추적하여 유지할 수 있다면 EL-DLL (delay lock loop with early minus late discriminator) 보다 추적편이를 줄일 수 있다. 본 논문에 이런 특성을 이용하는 추적편이 완화 기법을 제안하고, 모의실험을 통해 성능을 알아본다.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.8
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• pp.83-93
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• 2013

By comparing Wiener's MMSE on stochastic signal transmission with Shannon's mutual information first proved by C.E. Shannon in terms of information theory, connections between two approaches were investigated. What Wiener wanted to see in signal transmission in noisy channel is to try to capture fundamental limits for signal quality in signal estimation. On the other hands, Shannon was interested in finding fundamental limits of signal quantity that maximize the uncertainty in mutual information using the entropy concept in noisy channel. First concern of this paper is to show that in deriving limits of Shannon's point to point fundamental channel capacity, Shannon's mutual information obtained by exploiting MMSE combiner and Wiener filter's MMSE are interelated by integro-differential equantion. Then, At the meeting point of Wiener's MMSE and Shannon's mutual information the upper bound of spectral efficiency and the lower bound of energy efficiency were computed. Choosing a proper lattice-type code of a mod-${\Lambda}$AWGN channel model and MMSE estimation of ${\alpha}$ confirmed to lead to the fundamental Shannon capacity limits.