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Channel-Polarized multilevel coding for Low-Complexity Forward Error Correction

JOURNAL OF LIGHTWAVE TECHNOLOGY 2025年第10期43卷 4555-4563页

作者： Kakizaki, Takeshi Nakamura, Masanori Hamaoka, Fukutaro Kisaka, Yoshiaki NTT Network Innovat Labs Nippon Telegraph & Tel Corp Yokosuka 2390847 Japan

Digital coherent optical fiber communication systems adopt forward error correction (FEC) and multilevel modulation in accordance with transmission distance, data rate, and power consumption requirements. Bit-interleaved coded modulation (BICM) is practical coded modulation because of the simplicity of applying a binary code to converted binary-input memoryless channels (B-MCs) under a random bit-interleaver. The power consumption of soft-decision (SD) FEC has recently become a challenge due to transceiver power constraints. The multilevel coding (MLC) scheme efficiently reduces the decoding complexity, while the code design and complexity reduction depend on the modulation order. In this paper, we propose new binary codes for channel-polarized multilevel coding (CP-MLC) that convert multiple B-MCs to unreliable and reliable bit-channels and apply only SD-FEC to unreliable bit-channel to reduce the decoding complexity without depending on the modulation order. Systematic CP-MLC can also be used in probabilistically-shaped signals by using it in the component code of a probabilistic amplitude shaping scheme.

关键词： Decoding Modulation Complexity theory Symbols Codes Systematics Quadrature amplitude modulation Binary codes Encoding Reliability Forward error correction optical communication multilevel coding

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Probabilistic Shaped multilevel Polar coding for Wiretap Channel

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 2025年第4期43卷 1074-1088页

作者： Shen, Li Wu, Yongpeng Yuan, Peihong Xiao, Chengshan Xia, Xiang-Gen Zhang, Wenjun Shanghai Jiao Tong Univ Dept Elect Engn Shanghai 200240 Peoples R China Massachusetts Inst Technol MIT Res Lab Elect RLE Cambridge MA 02139 USA Lehigh Univ Dept Elect & Comp Engn Bethlehem PA 18015 USA Univ Delaware Dept Elect & Comp Engn Newark DE 19716 USA

A wiretap channel is served as the fundamental model of physical layer security techniques, where the secrecy capacity of the Gaussian wiretap channel is proven to be achieved by Gaussian input. However, there remains a gap between the Gaussian secrecy capacity and the secrecy rate with conventional uniformly distributed discrete constellation input, e.g. amplitude shift keying (ASK) and quadrature amplitude modulation (QAM). In this paper, we propose a probabilistic shaped multilevel polar coding scheme to bridge the gap. Specifically, the input distribution optimization problem for maximizing the secrecy rate with ASK/QAM input is solved. Numerical results show that the resulting sub-optimal solution can still approach the Gaussian secrecy capacity. Then, we investigate the polarization of multilevel polar codes for the asymmetric discrete memoryless wiretap channel, and thus propose a multilevel polar coding scheme integration with probabilistic shaping. It is proved that the scheme can achieve the secrecy capacity of the Gaussian wiretap channel with discrete constellation input, and satisfies the reliability condition and weak security condition. A security-oriented polar code construction method to natively satisfies the leakage-based security condition is also investigated. Simulation results show that the proposed scheme achieves more efficient and secure transmission than the uniform constellation input case over both the Gaussian wiretap channel and the Rayleigh fading wiretap channel.

关键词： Wireless networks Surveillance Oral communication Forensics Eavesdropping Security Encoding Codes Probabilistic logic Polar codes Physical layer security asymmetric wiretap channels multilevel coding polar codes probabilistic shaping

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multilevel coding Scheme for Integer-Forcing MIMO Receivers With Binary Codes

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2017年第8期16卷 5428-5441页

作者： Chae, Sung Ho Jang, Min Ahn, Seok-Ki Park, Jeongho Jeong, Cheol Samsung Elect Suwon 16677 South Korea Dongshin Univ Dept Energy IoT Naju 58245 South Korea

An integer-forcing (IF) linear multiple-input multiple-output (MIMO) receiver has recently been proposed, which is theoretically shown to achieve near capacity with almost the same complexity as that of conventional linear receivers. The key idea is that the receiver attempts to directly decode integer-linear combinations of codewords. To ensure that this sum-decoding operation is feasible, in previous works, lattice codes over Z(q) were employed. Although those codes can attain good theoretical performance, however, its implementation complexity can be considerably high in practice, especially when q is large to support high-order modulations. In this paper, we propose a practical multilevel coding scheme for IF MIMO, in which multilevel encoding composed of binary linear codes (q = 2) in conjunction with the natural mapping is employed on the transmitter side and multistage decoding adapted to the IF operation is employed on the receiver side. The performance of the proposed scheme is extensively evaluated both analytically and numerically, showing that the gain of IF over conventional receivers is indeed achievable in practical settings with almost the same complexity. Our results imply that the proposed IF MIMO can be an attractive solution for the 5G communications due to its ability of supporting high spectral efficiency with low complexity.

关键词： Binary code integer forcing linear receiver multilevel coding multiple-input multiple-output (MIMO)

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multilevel coding With Spatially Coupled Repeat-Accumulate Codes for High-Order QAM Optical Transmission

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JOURNAL OF LIGHTWAVE TECHNOLOGY 2019年第2期37卷 486-492页

作者： Koganei, Yohei Oyama, Tomofumi Sugitani, Kiichi Nakashima, Hisao Hoshida, Takeshi Fujitsu Labs Ltd Photon Res Ctr Kawasaki Kanagawa 2118588 Japan Fujitsu Kyushu Network Technol Ltd Fukuoka Fukuoka 8148588 Japan

We propose multilevel coding (MLC) with spatially coupled codes to increase the net coding gain (NCG) and reduce the power consumption of forward error correction (FEC) codes in high-order quadratic-amplitude modulation (QAM) optical transmissions. We optimized the degree distribution of the spatially coupled repeat-accumulate (SC-RA) codes by using density evolution to enhance the effect of spatial coupling with a limited code length. We constructed multilevel codes with the SC-RA codes and investigated their performance in numerical simulations. NCGs of 12.5, 13.2, and 13.7 dB were obtained for 16, 64, and 256 QAM. We found that MLC is more efficient in terms of circuit size and computational complexity than the conventional FEC configuration of bit-interleaved coded modulation (BICM). Moreover, its efficiency tends to increase as the modulation order increases. Our estimates suggest that the power consumed in the FEC process could be reduced to about half for 16 QAM, 35% for 64 QAM, and 15% for 256 QAM compared with when BICM is used to obtain similar NCG values.

关键词： Bit-interleaved coded modulation coherent optical communication density evolution forward error correction genetic algorithm multilevel coding multi-stage decoding quadrature amplitude modulation spatially coupled code spatially coupled repeat-accumulate code

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multilevel coding Schemes for Compute-and-Forward With Flexible Decoding

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IEEE TRANSACTIONS ON INFORMATION THEORY 2013年第11期59卷 7613-7631页

作者： Hern, Brett Narayanan, Krishna R. Texas A&M Univ Dept Elect & Comp Engn College Stn TX 77843 USA

We consider the design of coding schemes for the wireless two-way relaying channel when there is no channel state information at the transmitter. In the spirit of the compute-and-forward paradigm, we present a multilevel coding scheme that permits reliable computation (or, decoding) of a class of functions at the relay. The function to be computed (or decoded) is then chosen depending on the channel realization. We define such a class of functions which can be decoded at the relay using the proposed coding scheme and derive rates that are universally achievable over a set of channel gains when this class of functions is used at the relay. We develop our framework with general modulation formats in mind, but numerical results are presented for the case where each node transmits using 4-ary and 8-ary modulation schemes. Numerical results demonstrate that the flexibility afforded by our proposed scheme results in substantially higher rates than those achievable by always using a fixed function or considering only linear functions over higher order fields.

关键词： Compute-and-forward (CF) decode-and-forward multilevel coding network coding two-way relaying

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multilevel coding in M-ary DPSK/differential QAM high-speed optical transmission with direct detection

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JOURNAL OF LIGHTWAVE TECHNOLOGY 2006年第1期24卷 420-428页

作者： Djordjevic, IB Vasic, B Univ Arizona Dept Elect & Comp Engn Tucson AZ 85721 USA

A bandwidth- and power-efficient modulation scheme using M-ary differential phase-shift keying (DPSK)/differential quadrature amplitude modulation (DQAM) and low-density parity-check (LDPC) codes as component codes in a multilevel coding (MIX) is proposed for optical transmission systems with direct detection. An MIX scheme with 2 b/s/Hz spectral efficiency based on block-circulant component codes provides the coding gain of 12.3 dB when compared to uncoded 8-DPSK, and 8.3 dB when compared to uncoded 4-DPSK (QDPSK).

关键词： differential quadrature amplitude modulation (DQAM) low-density parity-check codes (LDPC) M-ary differential phase-shift keying (DPSK) Mach-Zehnder interferometer multilevel coding optical communications

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multilevel coding for multiple-antenna transmission

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2004年第1期3卷 203-208页

作者： Lampe, LHJ Schober, R Fischer, RFH Univ British Columbia Dept Elect & Comp Engn Vancouver BC V6T 1Z4 Canada Univ Erlangen Nurnberg Inst Informat Transmiss D-91058 Erlangen Germany

The application of powerful coding for transmission over multiple-input/multiple-output channels is discussed. The authors emphasize that as an immediate consequence. of the mutual information chain rule, multilevel coding (MLC) constitutes the optimum coded modulation scheme. On the other hand, simple bit-interleaved coded modulation (BICM) is only a convenient alternative for the case of two transmit and one receive antennas when combined with orthogonal space-time block codes. Starting from MLC, the authors further propose a hybrid coded modulation scheme, which favorably combines the advantages of MLC and BICM.

关键词： fading channels multilevel coding multiple-input/multiple-output (MIMO) transmission space-time coding

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multilevel coding with adaptive equalization and interleaving for fading channel

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1996年第9期E79A卷 1379-1385页

作者： Shohon, T Ogiwara, H Faculty of Engineering Nagaoka University of Technology Nagaoka-shi 940-21 Japan

In high-speed digital land mobile radio communication, communication quality is degraded by frequency selective fading that has intersymbol interference, It causes increase of bit error rate (BER). To decrease BER in the channel, this paper proposes a system with combined multilevel coding and adaptive equalization using interleaving. By using interleaving: the proposed system obtains time diversity effect. Furthermore the system realizes a type of decision feedback adaptive equalizer where a signal after multilevel decoder is fed back. These features of the system cause decrease of BER. The proposed system is compared with a similar system with a feedback signal before multilevel decoder. The average bit error rate of the proposed system is less than 1/100 with that of the compared system at average E(b)/N-o = 22 [dB] in a case of fading channel with one intersymbol interference.

关键词： multilevel coding equalization interleaving fading

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multilevel coding for Physical-Layer Security

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IEEE TRANSACTIONS ON COMMUNICATIONS 2022年第3期70卷 1999-2009页

作者： Pfeiffer, Johannes Fischer, Robert F. H. Ulm Univ Inst Commun Engn D-89081 Ulm Germany

In any transmission scheme, security against eavesdroppers is of importance. Contrary to classical encryption, security directly at the physical layer can be achieved by applying suited coding and modulation schemes. In this paper, coded modulation schemes, i.e., the use of higher-order constellations, is studied for generating both security against a wiretapper and reliability for the legitimate user. Specifically, a multilevel coding (MLC) scheme is considered. The influence of the constellation, in particular its cardinality and its dimensionality, on the gained security is assessed. As LSB component code, a practical secure coding scheme based on punctured LDPC codes is used. The security level for the employed LDPC code ensembles within MLC constructions is examined with an adapted density evolution technique. Results from numerical simulations cover the theoretical considerations and match with the derived asymptotic behavior. The results are compared to the situation when straightforwardly applying a binary code according to the BICM approach.

关键词： Security Encoding Codes Signal to noise ratio Modulation Measurement Lattices Bit-interleaved coded modulation density evolution Gaussian wiretap channel low-density parity-check codes multilevel coding physical-layer security security gap

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multilevel coding Schemes for Compute-and-Forward

Multilevel Coding Schemes for Compute-and-Forward

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IEEE International Symposium on Information Theory (ISIT)

作者： Hern, Brett Narayanan, Krishna Texas A&M Univ College Stn TX 77843 USA

ISBN: (纸本)9781457705953

We consider the design of coding schemes for the wireless two-way relaying channel when there is no channel state information at the transmitter. In the spirit of the compute and forward paradigm, we present a multilevel coding scheme that permits the recovery of a class of functions at the relay. We define such a class of functions and derive rates that are universally achievable over a set of channel gains when this class of functions is used at the relay. We develop our framework with general modulation formats in mind, but numerical results are presented for the case where each node transmits using the QPSK constellation. Numerical results with QPSK show that substantially higher rates are achievable with our proposed approach than those achievable by always using a fixed function or adapting the function at the relay but coding over GF(4).

关键词： Network coding multilevel coding two-way relaying compute-and-forward

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