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Rate Variable, Multi-binary Turbo codes with Controlled Error-Floor

IEEE TRANSACTIONS ON COMMUNICATIONS 2009年第5期57卷 1209-1214页

作者： Ferrari, Marco Bellini, Sandro Politecn Milan Dipartimento Elettron & Informat CNR Inst IEIIT Milan Italy

In this letter we propose rate variable turbo codes based on the parallel concatenation of tailbiting Recursive Systematic multi-binary (m-ary) convolutional codes. Rate variability is not achieved by puncturing, which can have adverse effects on the minimum distance of the code. Using a variable number of input lines of the encoder, we obtain several different overall rates ranging from 1/2 to 7/8. The most suitable Soft-In-Soft-Out decoding algorithm for these turbo codes is based on the Dual Reciprocal Code, which is very efficient for high rate codes. A particular interleaver design, namely the "backbone" interleaver, guarantees a high Hamming weight in codewords with information weight 2 and 3, as well as good minimum distances and fairly low multiplicities for higher information weights. Therefore, these codes have very low error floors.

关键词： Turbo codes non-binary codes dual codes variable rate codes

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Recursive Processing Algorithm for Low Complexity Decoding of Polar codes With Large Kernels

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IEEE TRANSACTIONS ON COMMUNICATIONS 2023年第9期71卷 5039-5050页

作者： Trifonov, Peter Karakchieva, Liudmila ITMO Univ Fac Informat Technol & Programming St Petersburg 197101 Russia

A reduced complexity algorithm is presented for computing the log-likelihood ratios (LLRs) arising in the successive cancellation (SC) decoder for polar codes with large kernels of arbitrary dimension. The proposed algorithm exploits a recursive trellis representation of the codes generated by submatrices of the polarization kernel and enables polar codes based on large kernels to be decoded with lower complexity compared to the codes based on the Arikan kernel with the same performance. Extensions to the case of non-binary kernels are presented.

关键词： Kernel Polar codes codes Complexity theory Maximum likelihood decoding Viterbi algorithm Symbols large kernels recursive maximum likelihood decoding non-binary codes

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High-Speed Parallel Decodable nonbinary Single-Error Correcting (SEC) codes

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IEEE TRANSACTIONS ON DEVICE AND MATERIALS RELIABILITY 2016年第1期16卷 30-37页

作者： Namba, Kazuteru Lombardi, Fabrizio Chiba Univ Grad Sch Adv Integrat Sci Chiba 2638522 Japan Northeastern Univ Dept Elect & Comp Engn Boston MA 02115 USA

This paper presents a novel construction scheme for nonbinary single-error correcting (SEC) codes that yields highspeed parallel decoding. The proposed scheme utilizes two methods, namely, Improved and Reordered;these methods can be also combined. Both of these methods reduce the number of 1's in the parity-check matrix (H-matrix) by reducing the 1's in every row vector. This results in a reduction in the gate depth in the syndrome generator, thus achieving a shorter delay time for parallel decoding. In the proposed Improved method, for a single b-bit byte (i.e., 2(b)-ary symbol) error correcting code, the submatrix of the H-matrix corresponding to every b-bit byte is multiplied with a regular matrix. The so-called improved submatrix is generated using a heuristic (greedy) algorithm. The proposed Reordered method selects the correct b-bit bytes for deletion when shortening is performed. Simulation results show that the proposed scheme accomplishes a faster parallel decoding time than existing schemes. Furthermore, the proposed scheme is applicable to any class of linear SEC codes, whereas existing schemes are applicable only to specific codes. Extensive simulation results are provided to substantiate the viability of the proposed codes for faster parallel decoding (albeit incurring for most cases in modest increases of area and power dissipation due to additional circuitry).

关键词： Error correcting code (ECC) single error correction (SEC) non-binary codes parallel decoder

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Recursive Construction of k-Ary Uniquely Decodable codes for Multiple-Access Adder Channel 15

Recursive Construction of <i>k</i>-Ary Uniquely Decodable Co...

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15th International Symposium on Information Theory and its Applications (ISITA)

作者： Lu, Shan Hou, Wei Cheng, Jun Kamabe, Hiroshi Gifu Univ Dept Elect Elect & Comp Engn Gifu Japan Xidian Univ State Key Lab ISN Xian Shaanxi Peoples R China Doshisha Univ Dept Intelligent Informat Engn & Sci Kyotanabe Japan

A recursive construction of k-ary uniquely decodable multiuser codes is proposed for use in a noiseless multiple-access adder channel. The code rates of the proposed codes are higher than those of previous uniquely de... 详细信息

ISBN: (纸本)9784885523182

关键词： uniquely decodable codes non-binary codes multiple-access adder channel

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Denser High-Order Fibonacci codes

Denser High-Order Fibonacci Codes

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Data Compression Conference (DCC)

作者： Klein, Shmuel T. Shapira, Dana Bar Ilan Univ Dept Comp Sci IL-52900 Ramat Gan Israel Ariel Univ Dept Comp Sci IL-40700 Ariel Israel

ISBN: (纸本)9798350385885;9798350385878

Previous work on non-binary Fibonacci codes is extended by the presentation of a new family of universal codes having the additional advantage of admitting more codewords for a given large enough length. These denser codes also share the other properties of instantaneous decipherability and robustness against transmission errors, and are proposed as an alternative to compress lists of very large integers, like those used in cryptography.

关键词： Fibonacci codes non-binary codes universal codes

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Low-Lee-Density Parity-Check codes

Low-Lee-Density Parity-Check Codes

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IEEE International Conference on Communications (IEEE ICC) / Workshop on NOMA for 5G and Beyond

作者： Santini, Paolo Battaglioni, Massimo Chiaraluce, Franco Baldi, Marco Persichetti, Edoardo Univ Politecn Marche Dipartimento Ingn Informaz Ancona Italy Florida Atlantic Univ Dept Math Sci Boca Raton FL 33431 USA

ISBN: (纸本)9781728150895

We introduce a new family of linear block codes over Z(q) that we name low-Lee-density parity-check (LLDPC) codes. These codes, which are embedded with the Lee metric, are characterized by a parity-check matrix whose rows and columns have low Lee weight. We propose general constructions of LLDPC codes and devise an efficient iterative decoding algorithm for them, with complexity that grows linearly with the code length. We assess the error rate performance of these codes through numerical simulations.

关键词： Error correcting codes Lee metric LLDPC codes non-binary codes

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A Serial Concatenation of binary-Input nonbinary-Output Convolutional Code and Recursive Convolutional Lattice Code

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IEEE ACCESS 2018年 6卷 24809-24817页

作者： Matsumine, Toshiki Ochiai, Hideki Yokohama Natl Univ Dept Elect & Comp Engn Yokohama Kanagawa 2408501 Japan

The recently proposed recursive convolutional lattice code (RCLC) can form a signal with pseudo-Gaussian constellations, and their parallel concatenation is shown to approach the Shannon limit. A practical limitation is that its input symbol is limited to L-2-ary quadrature amplitude modulation (QAM), which has non-power-of-two constellation points when L is chosen from the odd numbers. Therefore, encoding binary information by the RCLC is not straightforward. Furthermore, the information rate is limited to log(2) L bits per complex dimension due to their parallel concatenation. In this paper, we tackle these issues by introducing a serial concatenation of binary-input nonbinary-output convolutional code (CC) and the RCLC, where the outer CC outputs an L-ary symbol that is matched to the input of the inner RCLC. We demonstrate that even with L = 3, the proposed approach can achieve 2 bits per complex dimension and still is able to approach the Shannon limit with lower decoding complexity compared with its parallel concatenation counterpart. As is demonstrated through theoretical analysis, the major practical drawback of the constellation generated by the RCLC is its Gaussian-like distribution, which has large peak-to average power ratio. Therefore, we further introduce an approach to reduce the signal dynamic range for the proposed system. It is shown that a remarkable gain can be achieved in terms of capacity compared with the conventional QAM signals under the constraint of comparable power amplifier efficiency.

关键词： Serial concatenation non-binary codes signal codes coded modulation constellation shaping

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Exploring and Experimenting With Shaping Designs for Next-Generation Optical Communications

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JOURNAL OF LIGHTWAVE TECHNOLOGY 2018年第22期36卷 5298-5308页

作者： Jardel, Fanny Eriksson, Tobias A. Measson, Cyril Ghazisaeidi, Amirhossein Buchali, Fred Idler, Wilfried Boutros, Joseph J. Nokia Bell Labs F-91620 Paris France Natl Inst Informat & Commun Technol Quantum ICI Adv Dev Ctr Tokyo 1848795 Japan Nokia Bell Labs D-70435 Stuttgart Germany Texas A&M Univ Doha 23874 Qatar

A class of circular 64-QAM that combines "geometric" and "probabilistic" shaping aspects is presented. It is compared to square 64-QAM in back-to-back, single-channel, and wavelength division multiplexing (WDM) transmission experiments. First, for the linear additive white Gaussian noise channel model, it permits to operate close to the Shannon limits for a wide range of signal-to-noise ratios. Second, WDM simulations over several hundreds of kilometers show that the obtained signal-to-noise ratios are equivalent to-or slightly exceed-those of probabilistic shaped 64-QAM. Third, for real-life validation purpose, an experimental comparison with unshaped 64-QAM is performed where 28% distance gains are recorded when using 19 channels at 54.2 GBd. This again is in line-or slightly exceeds-the gains generally obtained with probabilistic shaping. Depending upon implementation requirements (core forward-error correcting scheme for example), the investigated modulation schemes may be key alternatives for next-generation optical systems.

关键词： Communications theory coded modulation non-uniform signaling probabilistic amplitude shaping non-binary codes BICM optical networks nonlinear optics

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A General non-binary LDPC Code Optimization Framework Suitable for Dense Flash Memory and Magnetic Storage

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 2016年第9期34卷 2402-2415页

作者： Hareedy, Ahmed Lanka, Chinmayi Dolecek, Lara Univ Calif Los Angeles Dept Elect Engn Los Angeles CA 90095 USA

Transmission channels underlying modern dense storage systems, e.g., Flash memory and magnetic recording (MR) systems, significantly differ from canonical channels, like additive white Gaussian noise (AWGN) channels. While existing low-density parity-check (LDPC) codes optimized for symmetric, AWGN-like channels are being actively considered for Flash applications, we demonstrate that, due to channel asymmetry, such approaches are inadequate. We introduce a refined definition of absorbing sets, which we call general absorbing sets of type two (GASTs), and study the combinatorial properties of GASTs. We then present the weight consistency matrix (WCM), which succinctly captures key properties in a GAST. Furthermore, we show how to customize the WCM definition such that it suits other special subclasses of GASTs. Based on these new concepts, we then develop a new, general combinatorial code optimization framework, which we call the WCM framework, and demonstrate its effectiveness on the realistic highly-asymmetric normal-Laplace mixture (NLM) Flash channel. Moreover, we show that our framework can be customized to optimize non-binary LDPC (NB-LDPC) codes for other asymmetric channels, channels with memory (incorporated in MR systems), and canonical symmetric channels. For all the channels we have simulated NB-LDPC codes over, the codes optimized using the WCM framework enjoy at least 1 order, and up to nearly 2 orders of magnitude performance gain in the uncorrectable bit error rate (UBER) or the frame error rate (FER) relative to the unoptimized codes. Our simulations also show that codes optimized for symmetric channels are not the best choice for asymmetric channels.

关键词： LDPC codes non-binary codes absorbing sets weight consistency matrices Flash memory asymmetric channels magnetic recording error floor

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Challenges and Some New Directions in Channel Coding

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JOURNAL OF COMMUNICATIONS AND NETWORKS 2015年第4期17卷 328-338页

作者： Arikan, Erdal ul Hassan, Najeeb Lentmaier, Michael Montorsi, Guido Sayir, Jossy Bilkent Univ Elect Elect Engn Dept Ankara Turkey Tech Univ Dresden Vodafone Chair Mobile Commun Dresden Germany Lund Univ Dept Elect & Informat Technol S-22100 Lund Sweden Politecn Torino I-10129 Turin Italy Univ Cambridge Dept Engn Cambridge CB2 1TN England

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, non-binary LDPC codes, and polar coding.

关键词： Channel polarization low-density parity-check (LDPC) codes non-binary codes polar codes spatial coupling

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