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On Decoding of the (89, 45, 17) Quadratic Residue Code

IEEE TRANSACTIONS ON COMMUNICATIONS 2013年第3期61卷 832-841页

作者： Wang, Lin Li, Yong Truong, Trieu-Kien Lin, Tsung-Ching Xiamen Univ Dept Commun Engn Xiamen 361005 Peoples R China Chongqing Univ Posts & Telecommunicat CQUPT Chongqing Peoples R China I Shou Univ Dept Informat Engn Kaohsiung 84001 Taiwan Natl Sun Yat Sen Univ Dept Comp Sci & Engn Taipei Taiwan

In this paper, Three decoding methods of the (89, 45, 17) binary quadratic residue (QR) code to be presented are hard, soft and linear programming decoding algorithms. Firstly, a new hybrid algebraic decoding algorithm for the (89, 45, 17) QR code is proposed. It uses the Laplace formula to obtain the primary unknown syndromes, as done in Lin et al.'s algorithm when the number of errors v is less than or equal to 5, whereas Gaussian elimination is adopted to compute the unknown syndromes when v >= 6. Secondly, an appropriate modification to the algorithm developed by chase is also given in this paper. Therefore, combining the proposed algebraic decoding algorithm with the modified chase-II algorithm, called a new soft-decision decoding algorithm, becomes a complete soft decoding of QR codes. Thirdly, in order to further improve the error-correcting performance of the code, linear programming (LP) is utilized to decode the (89, 45, 17) QR code. Simulation results show that the proposed algebraic decoding algorithm reduces the decoding time when compared with Lin et al.'s hard decoding algorithm, and thus significantly reduces the decoding complexity of soft decoding while maintaining the same bit error rate (BER) performance. Moreover, the LP-based decoding improves the error-rate performance almost without increasing the decoding complexity, when compared with the new softdecision decoding algorithm. It provides a coding gain of 0.2 dB at BER = 2 x 10(-6).

关键词： Berlekamp-Massey algorithm Gaussian elimination quadratic residue code chase algorithm linear programming

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A sufficient condition for ruling out some useless test error patterns in iterative decoding algorithms

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1998年第2期E81A卷 321-326页

作者： Koumoto, T Kasami, T Lin, S Nara Inst Sci & Technol Grad Sch Informat Sci Ikoma 6300101 Japan Univ Hawaii Manoa Dept Elect Engn Honolulu HI 96822 USA

In an iterative decoding algorithm, such as chase Type-II decoding algorithm and its improvements, candidate codewords for a received vector are generated for test based on a bounded-distance decoder and a set of test error patterns. It is desirable to remove useless test error patterns in these decoding algorithms. This paper presents a sufficient condition for ruling out some useless test error patterns. If this condition holds for a test error patterns e, then e can not produce a candidate codeword with a correlation metric larger than those of the candidate codewords generated already and hence e is useless. This significantly reduces the decoding operations in chase type-II decoding algorithm or decoding iterations in its improvements.

关键词： binary linear code chase algorithm iterative decoding sufficient condition optimality test

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Near Shannon Limit and Low Peak to Average Power Ratio Turbo Block Coded OFDM

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IEEE TRANSACTIONS ON COMMUNICATIONS 2011年第8期59卷 2042-2045页

作者： Sabbaghian, Maryam Kwak, Yongjun Smida, Besma Tarokh, Vahid Harvard Univ Sch Engn & Appl Sci Cambridge MA 02138 USA

In this paper, we present an advanced solution for the long standing problem of large peak to average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. Although the design of low PAPR codewords has been extensively studied and the existence of asymptotically good codes with low PAPR is also proven, still no code has been constructed to satisfy all requirements. The main goal of the paper is to develop a coding scheme that not only generates low PAPR codewords, but it also performs relatively close to the Shannon limit. We achieve this goal by implementing a time-frequency turbo block coded OFDM. In this scheme, we design the frequency domain component to have a tightly bounded PAPR. The time domain component code is designed to obtain good performance while the decoding algorithm has reasonable complexity. Through comparative performance evaluation we show that utilizing the proposed method, we achieve considerable improvement in terms of PAPR while we slightly loose the performance compared to capacity achieving codes with similar overall block length.

关键词： Time-frequency turbo block code chase algorithm OFDM PAPR Reed-Muller code

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Efficient Low-Complexity Decoding of CCSDS Reed-Solomon Codes Based on Justesen's Concatenation

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IEEE ACCESS 2019年 7卷 49596-49603页

作者： Elagooz, Ranya Salah Mahran, Ashraf Gasser, Safa Aboul-Dahab, Mohamed Arab Acad Sci Technol & Maritime Transport Elect & Commun Dept Cairo 11361 Egypt Natl Author Remote Sensing & Space Sci Cairo 11361 Egypt Mil Tech Coll Avion Dept Cairo 11331 Egypt

Forward error correction (FEC) is a key capability in modern satellite communications that provide the system designer with the needed flexibility to comply with the different applications' requirements. Reed-Solomon (RS) codes are well known for their ability to optimize between the system power, bandwidth, data rate, and the quality of service. This paper introduces an efficient decoding scheme for decoding the RS codes adhering to the Consultative Committee for Space Data Systems (CCSDS) standards based on Justesen's construction of concatenation. To maintain the standard output size, the proposed scheme first encodes every m - 1 bits using the single-parity-check (SPC) code, while the RS code encodes K SPC codewords into N symbols that are of the same size as CCSDS standard. Decoding on the inner SPC code is based on maximum-likelihood decoding Kaneko algorithm, while for the proposed coding scheme, the reduced test-pattern chase algorithm is adapted for decoding the outer RS code. The simulation results show the coding gains of 1.4 and 7 dB compared with the algebraic decoding of RS codes over the AWGN and Rayleigh fading channels, respectively. Moreover, the adopted reduced test-pattern chase algorithm for decoding the RS code achieves an overall complexity reduction of 40% compared with the conventional chase decoding algorithm.

关键词： CCSDS chase algorithm concatenated codes Justesen code Reed-Solomon code single-parity-check

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Implication and axiomatization of functional and constant constraints

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ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE 2016年第3-4期76卷 251-279页

作者： Hellings, Jelle Gyssens, Marc Paredaens, Jan Wu, Yuqing Hasselt Univ Fac Sci Martelarenlaan 42 B-3500 Hasselt Belgium Transnat Univ Limburg Martelarenlaan 42 B-3500 Hasselt Belgium Univ Antwerp Dept Math & Comp Sci Campus MiddelheimBldg GMiddelheimlaan 1 B-2020 Antwerp Belgium Pomona Coll Dept Comp Sci 185 E 6th St Claremont CA 91711 USA

Akhtar et al. introduced equality-generating constraints and functional constraints as a first step towards dependency-like integrity constraints for RDF data [3]. Here, we focus on functional constraints. Since the usefulness of functional constraints is not limited to the RDF data model, we study the functional constraints in the more general setting of relations with arbitrary arity. We further introduce constant constraints and study the functional and constant constraints combined. Our main results are sound and complete axiomatizations for the functional and constant constraints, both separately and combined. These axiomatizations are derived using the chase algorithm for equality-generating constraints. For derivations of constant constraints, we show how every chase step can be simulated by a bounded number of applications of inference rules. For derivations of functional constraints, we show that the chase algorithm can be normalized to a more specialized symmetry-preserving chase algorithm performing so-called symmetry-preserving steps. We then show how each symmetry-preserving step can be simulated by a bounded number of applications of inference rules. The axiomatization for functional constraints is in particular applicable to the RDF data model, solving a major open problem of Akhtar et al.

关键词： Functional constraints Constant constraints chase algorithm Axiomatization

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Low-Complexity High-Speed Soft-Hard Decoding for Turbo-Product Codes 37

Low-Complexity High-Speed Soft-Hard Decoding for Turbo-Produ...

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37th IEEE International Conference on Electronics and Nanotechnology (ELNANO)

作者： Krainyk, Yaroslav Perov, Vladislav Musiyenko, Maksym Petro Mohyla Black Sea Natl Univ Dept Comp Engn Mykolaiv Ukraine

ISBN: (纸本)9781538617014

Combined (soft-hard) method for decoding block turbo-product codes is proposed in the paper. The method allows leveraging advantages of soft input data usage with the speed of hard-decoding procedure. The main peculiarity of the method is rule-based decoding stage. The proposed approach simplifies calculation procedure and reaches better correction ability than hard-decision decoder. Mathematical model of investigated method has been tested with the set of codes based on product of extended Hamming codes. Testing has confirmed correctness of the combined decoding method.

关键词： combined method TPC decoding rule-based method chase algorithm

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Lowered-Complexity Soft Decoding of Generalized LDPC Codes over AWGN Channels 12

Lowered-Complexity Soft Decoding of Generalized LDPC Codes o...

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12th International Conference on Computer Engineering and Systems (ICCES)

作者： Elsanadily, Sherif I. Mahran, Ashraf M. Elghandour, Osama M. Helwan Univ Fac Engn Dept Commun & Elect Cairo Egypt Mil Tech Coll Dept Commun & Avion Cairo Egypt

ISBN: (纸本)9781538611913

This paper presents a lowered complexity version of a reliability-based iterative decoding algorithm for Generalized Low Density Parity Check (GLDPC) codes with BCH constituent codes using Soft-Input Soft-Output (SISO) chase-II algorithm. Applied to Gallager-based global LDPC code, it shows that the proposed algorithm, when employed on GLDPC with the multi-error correction BCH subcodes, reduces the complexity of the conventional Soft-Decision Decoding (SDD) with chase algorithm at a cost of slight degradation in the error performance. The approach is built on eliminating the employment of the chase SISO decoder at the Generalized Check Nodes (GCNs) where the expected number of errors is within the correction capability of the Hard-Decision Decoder (HDD). As a case study, the decoder is considered under AWGN channel and Simulation results are presented showing the complexity and performance of the conventional and proposed algorithms.

关键词： Iterative decoding APP decoding Hamming codes chase algorithm low-density parity-check codes

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Combining Provenance Management and Schema Evolution 7th

Combining Provenance Management and Schema Evolution

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7th International Provenance and Annotation Workshop (IPAW)

作者： Auge, Tanja Heuer, Andreas Univ Rostock Rostock Germany

ISBN: (纸本)9783319983790;9783319983783

The combination of provenance management and schema evolution using the chase algorithm is the focus of our research in the area of research data management. The aim is to combine the construction of a chase inverse mapping to calculate the minimal part of the original database - the minimal sub-database - with a chase-based schema mapping for schema evolution.

关键词： chase algorithm Data provenance Schema evolution Data evolution Schema mapping chase inverse

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Soft-Decision RS Decoding algorithm and Its DSP Implementation in DSSS Systems

Soft-Decision RS Decoding Algorithm and Its DSP Implementati...

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3rd International Conference on Wireless Communications, Networking and Mobile Computing (WiCOM 2007)

作者： Bu Xiang-yuan Zhu Pei-pei Beijing Inst Technol Dept Elect Engn Beijing 100081 Peoples R China

ISBN: (纸本)9781424413119

A soft-decision Reed-Solomon(RS) decoding algorithm is introduced. chase algorithm is employed and an improved chase algorithm is presented. Hard-decision and soft-decision decoding are tested under Additive White Gaussian Noise(AWGN) channel using BPSK. Simulation results show that larger coding gain is obtained by using soft-decision decoding and the tradeoff between error performance and decoding complexity using improved chase algorithm is provided. Finally, DSP implementation scheme of soft-decision RS decoder in Direct Sequence Spread Spectrum(DSSS) systems is proposed.

关键词： Reed-Solomon codes soft-decision decoding chase algorithm DSP

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FPGA Implementation of Turbo Product CODEC

FPGA Implementation of Turbo Product CODEC

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IEEE Region 10 Colloquium/3rd International Conference on Industrial and Information Systems

作者： Chakraborty, Susmita Radhika, T. Chakrabarti, Saswat Indian Inst Technol GS Sanyal Sch Telecommun Kharagpur 721302 W Bengal India

ISBN: (纸本)9781424428052

Error control coding plays a vital role to maintain data accuracy across noisy channel. Turbo Product Code is a high performance error correcting code. It can be used in any communication system where a significant power saving is required or operating signal to noise ratio is very poor. This paper presents an implementation of a turbo product CODEC with Reed-Muller (16, 5, 8) as constituent codes. The design has been simulated and synthesized successfully in Xilinx Integrated Software Environment.

关键词： chase algorithm error control coding iterative decoding turbo product code

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