• 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.

• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.17 no.8
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• pp.2157-2169
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• 2023

In order to handle the problem that puncture patterns will change the position distribution of original information bits and frozen bits in polar codes, which affects performance of puncture polar codes further, a minimum row weight and polar spectrum based puncture polar codes construction algorithm (called PA-MRWP) is proposed in this paper. The algorithm calculates row weight of generator matrix and sorts the row weight in ascending order first. Next, the positions with the minimum row weight are selected as initial puncture positions. If the rows with the same row weight cannot all be punctured, polar spectrum based auxiliary puncture scheme is used. In sub-channels with the same row weight, rows corresponding to the polarized sub-channels with higher reliability are selected as puncture positions to construct puncture vector, and the reliability is calculated based on polar spectrum. It is actually a two-step selection strategy, the proposed minimum row weight puncture (MRWP) algorithm is used for primary selection and polar spectrum based auxiliary puncture is used for adjustment. Simulation results show that, compared with worst quality puncture (WQP) algorithm, the proposed PA-MRWP algorithm and Gaussian approximation-aided minimum row weight puncture (GA-MRWP) algorithm provide gains of about 0.46 dB and 0.29 dB at bit error rate (BER) of 10^-4, respectively when code length N=400, code rate R=1/2. In addition, the proposed puncture algorithms improve the BER performance significantly with respect to quasi-uniform puncture (QUP) algorithm.

• Journal of Korea Society of Digital Industry and Information Management
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• v.11 no.3
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• pp.45-51
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• 2015

In this paper, we discuss the belief propagation decoding algorithm for polar codes. The performance of Polar codes for shorter lengths is not satisfactory. Motivated by this, we propose a novel technique to improve its performance at short lengths. We showed that the probability of messages passed along the factor graph of polar codes, can be increased by multiplying the current message of nodes with their previous message. This is like a feedback path in which the present signal is updated by multiplying with its previous signal. Thus the experimental results show that performance of belief propagation polar decoder can be improved using this proposed technique. Simulation results in binary-input additive white Gaussian noise channel (BI-AWGNC) show that the proposed belief propagation polar decoder can provide significant gain of 2 dB over the original belief propagation polar decoder with code rate 0.5 and code length 128 at the bit error rate (BER) of $10^{-4}$.

• 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.

• ETRI Journal
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• v.40 no.3
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• pp.291-302
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• 2018

The deployment of an incremental hybrid decode-amplify and forward relaying scheme is a promising and superior solution for cellular networks to meet ever-growing network traffic demands. However, the selection of a suitable relaying protocol based on the signal-to-noise ratio threshold is important in realizing an improved quality of service. In this paper, an incremental hybrid relaying protocol is proposed using polar codes. The proposed protocol achieves a better performance than existing turbo codes in terms of capacity. Simulation results show that the polar codes through an incremental hybrid decode-amplify-and-forward relay can provide a 38% gain when ${\gamma}_{th(1)}$ and ${\gamma}_{th(2)}$ are optimal. Further, the channel capacity is improved to 17.5 b/s/Hz and 23 b/s/Hz for $2{\times}2$ MIMO and $4{\times}4$ MIMO systems, respectively. Monte Carlo simulations are carried out to achieve the optimal solution.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.7
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• pp.3156-3167
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• 2020

One drawback of polar codes is that they are not universal, that is, to achieve optimal performance, different polar codes are required for different kinds of channel. This paper proposes a polar code construction scheme for Nakagami-m fading channel. The scheme fully considers the characteristics of Nakagami-m fading channel, and uses the optimized Bhattacharyya parameter bounds. The constructed code is applied to an orthogonal frequency division multiplexing (OFDM) system over Nakagami-m fading channel to prove the performance of polar code. Simulation result shows the proposed codes can get excellent bit error rate (BER) performance with successive cancellation list (SCL) decoding. For example, the designed polar code with cyclic redundancy check (CRC) aided SCL (L = 8) decoding achieves 1.1dB of gain over LDPC at average BER about 10^-5 under 4-quadrature amplitude modulation (4QAM) while the code length is 1024, rate is 0.5.

• 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.

• 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 Communications and Networks
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• v.17 no.4
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• pp.328-338
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• 2015

Three areas of ongoing research in channel coding are surveyed, and recent developments are presented in each area: Spatially coupled low-density parity-check (LDPC) codes, nonbinary LDPC codes, and polar coding.