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Vector bundles on curves over F_q and algebraic codes

FINITE FIELDS AND THEIR APPLICATIONS 2008年第4期14卷 1101-1107页

作者： Ballico, E. Univ Trent Dept Math I-38050 Povo TN Italy

Let C be a smooth, geometrically connected, projective curve of genus g >= 2 defined over F-q. Here we follow a recent paper of Savin and study the parameters (size, dimension, minimal distance) of algebraic codes constructed using vector bundles E on C. We need to construct vector bundles defined over F, and with certain numerical invariants (degree, rank h(0)(C, E), order of 1-stability). (C) 2008 Elsevier Inc. All rights reserved.

关键词： Vector bundle algebraic code

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Efficient encoding of excitation codes using trained partial algebraic codebook

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IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 1998年第6期E81D卷 612-615页

作者： Lee, YK Lee, HS Gray, RM Korea Adv Inst Sci & Technol Dept Informat & Commun Engn Seoul South Korea

An efficient encoding method of excitation codes using a partial algebraic codebook (PAC) is proposed. Since the conventional algebraic code excited linear prediction (ACELP) encodes the positions and signs of all excitation pulses separately, the bits required for encoding excitation codes lake a large portion of the total bit rate. Vector quantization (VQ) of the positions and signs of the excitation pulses results in a PAC. Using PAC instead of the full set of algebraic codes, we can reduce the bits required to encode the excitation codes while maintaining the output speech quality. An iterative training algorithm is proposed to obtain the suboptimal PAC by modifying the Lloyd algorithm. Simulation results show that considerable bit savings can be obtained with only a small amount of degradation in the segmental signal to noise ratio (SEGSNR).

关键词： algebraic code ACELP speech coding

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An Efficient Detection Algorithm for algebraic coded V-BLAST Systems

An Efficient Detection Algorithm for Algebraic Coded V-BLAST...

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

作者： Jin, Xiufeng Bi, Guangguo Southeast Univ Natl Mobile Commun Res Lab Nanjing Peoples R China

ISBN: (纸本)9781424413119

The V-BLAST multiple antenna architecture is a well-known method for achieving high spectral efficiency over a rich-scattering environment In V-BLAST systems, detection is performed layer by layer in a successive way. However, due to error propagation, the system performance Is largely constrained by the accuracy of the lower layers detected first. In order to improve the performance of the low layers, in this paper, we give an algebraic coded V-BLAST scheme, which employs algebraic code In the lower layers of V-BLAST systems. At the receiver, an efficient detection algorithm which combines list sphere decoder and sorted QR decomposition successive Interference cancellation Is proposed. Simulation results show that the new detection method significantly outperforms the conventional ZF-VBLAST and MMSE-VBLAST schemes.

关键词： algebraic code V-BLAST diversity list sphere decoder ML detection

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Analysis of the distribution of the number of erasures correctable by a binary linear code and the link to low-weight codewords

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IET COMMUNICATIONS 2007年第3期1卷 539-548页

作者： Tomlinson, M. Tjhai, C. Cai, J. Ambroze, M. Univ Plymouth Plymouth PL4 8AA Devon England

The number and weight of low-weight codewords of a binary linear code determine the erasure channel performance. Analysis is given of the probability density function of the number of erasures correctable by the code in terms of the weight enumerator polynomial. For finite-length codes, zero erasure decoder error rate is impossible, even with maximum-distance-separable (MDS) codes and maximum-likelihood decoding. However, for codes that have binomial weight spectra, for example BCH, Goppa and double-circulant codes, the erasure correction performance is close to that of MDS codes. One surprising result is that, for many (n, k) codes, the average number of correctable erasures is almost equal to n - k, which is significantly larger than d(min) - 1. For the class of iteratively decodable codes (LDPC and turbo codes), the erasure performance is poor in comparison to algebraic codes designed for maximum d,i. It is also shown that the turbo codes that have optimised d(min) have significantly better performance than LDPC codes. A probabilistic method, which has considerably smaller search space than that of the generator matrix-based methods, is presented to determine the d(min) of a linear code using random erasure patterns. Using this approach, it is shown that there are (168, 84, 24) and (216, 108, 24) quadratic double-circulant codes.

关键词： quadratic double-circulant code maximum-distance-separable code erasure distribution algebraic codes finite-length code binary linear code error correction codes turbo codes statistical distributions binomial weight spectra probabilistic method binary codes erasure correction performance MDS turbo code polynomials algebraic code codeword weight enumerator polynomial erasure channel linear codes

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High Performance Of Parallel Concatenated code

High Performance Of Parallel Concatenated Code

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3rd IEEE International Conference on Computer Science and Information Technology (ICCSIT)

作者： Zhao, Qian Zhou, Liang Wen, Hong Xu, Fen Huang, Chen Univ Elect Sci & Technol China Commun Nation Key Lab Chengdu Peoples R China

ISBN: (纸本)9781424455379

In this paper, we introduce a kind of high performance of concatenated code that is called parallel concatenated code. Comparing to conventional serial concatenated code, it has more matching room and higher adaptability. Moreover, burst of errors which are aroused by noise are beautiful restrained. For certifying the superiority and practicability, we research a parallel concatenated code by combining the outer algebraic code with the inner Low density Parity Check (LDPC) code. The bit error rate (BER) may be as low as 10(-22) when Signal Noise Ratio (SNR) is 3.9dB. In the high speed 100Gp/s optical communication system, it will play a significant role.

关键词： parallel concatenated code LDPC code algebraic code lower BERs

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Efficient Decoding of Block Turbo codes

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JOURNAL OF COMMUNICATIONS AND NETWORKS 2018年第4期20卷 345-353页

作者： Son, Jaeyong Kong, Jun Jin Yang, Kyeongcheol Samsung Elect Co Ltd Memory Business Controller Dev Team Suwon South Korea Pohang Univ Sci & Technol POSTECH Dept Elect Engn Pohang South Korea

Block turbo codes (BTCs) under iterative decoding are product codes showing excellent performance with reasonable complexity, whose component codes are conventionally decoded in two stages. The Chase algorithm is employed in the first stage to make a list of candidate codewords from the received vector, while the extrinsic information for iterative decoding is generated in the second stage. In this paper, we propose an efficient decoding algorithm for BTCs. The proposed algorithm can avoid a number of unnecessary hard-decision decoding operations by imposing two conditions on the Chase algorithm. Also, it simply computes the extrinsic information for the decision codeword. Numerical results demonstrate that the proposed algorithm has not only much lower computational complexity, but also a little better performance than the conventional decoding scheme based on the Chase algorithm. Furthermore, it can provide a trade-off between the performance and the computational complexity of BTCs by properly selecting a decoding parameter.

关键词： algebraic code block turbo codes (BTCs) Chase algorithm efficient decoding product codes

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On numerical semigroups and the redundancy of improved codes correcting generic errors

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DESIGNS codeS AND CRYPTOGRAPHY 2009年第2期53卷 111-118页

作者： Bras-Amoros, Maria Univ Rovira & Virgili Tarragona Catalonia Spain

We introduce a new sequence tau associated to a numerical semigroup similar to the nu sequence used to define the order bound on the minimum distance and to describe the Feng-Rao improved codes. The new sequence allows a nice description of the optimal one-point codes correcting generic errors and to compare them with standard codes and with the Feng-Rao improved codes. The relation between the tau sequence and the nu sequence gives a new characterization of Arf semigroups and it is shown that the tau sequence of a numerical semigroup unequivocally determines it.

关键词： algebraic code Generic error Numerical semigroup

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List decoding of maximal order codes over number fields

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FINITE FIELDS AND THEIR APPLICATIONS 2024年 93卷

作者： Kourani, Nasim Abdi Khodaiemehr, Hassan Nikmehr, Mohammad Javad KN Toosi Univ Technol Fac Math Dept Pure Math POB 167653381 Tehran Iran KN Toosi Univ Technol Fac Math Dept Comp Sci & Stat POB 167653381 Tehran Iran Inst Res Fundamental Sci IPM Sch Math Tehran 193955746 Iran

In this paper, we provide two distinct list decoding algorithms tailored for specific classes of maximal order number field codes. The first algorithm focuses on the unit codes, while the second algorithm is dedicated to the Arakelov divisor-based number field codes. These codes were originally introduced by Maire and Oggier. To achieve our decoding goals, we utilize the list decoding algorithm for general number field codes proposed by Biasse and Quintin. Our approach involves carefully calculating the required parameter B from Biasse and Quintin's algorithm, and adjusting the returned list to satisfy the desired conditions. For unit codes, we consider two cases: when the underlying number field is totally real and when it has an arbitrary signature. We separate these cases because the parameter B can be improved in the totally real scenario. Additionally, we present our list decoding algorithm for Arakelov divisor-based number field codes, focusing on number fields with arbitrary signatures.(c) 2023 Elsevier Inc. All rights reserved.

关键词： algebraic code List decoding Number field code Arakelov divisor Unit code

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An Efficient Detection Algorithm for algebraic coded V-BLAST Systems

An Efficient Detection Algorithm for Algebraic Coded V-BLAST...

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第三届IEEE无线通讯、网络技术暨移动计算国际会议

作者： Xiufeng Jin Guangguo Bi National Mobile Communications Research Lab. Southeast University Nanjing China National Mobile Communications Research Lab.Southeast University Nanjing China

The V-BLAST multiple antenna architecture is a wellknown method for achieving high spectral efficiency over a richscattering environment. In V-BLAST systems, detection is performed layer by layer in a successive way. However, due to error propagation, the system performance is largely constrained by the accuracy of the lower layers detected first. In order to improve the performance of the low layers, in this paper, we give an algebraic coded V-BLAST scheme, which employs algebraic code in the lower layers of V-BLAST systems. At the receiver, an efficient detection algorithm which combines list sphere decoder and sorted QR decomposition successive interference cancellation is proposed. Simulation results show that the new detection method significantly outperforms the conventional ZF-VBLAST and MMSE-VBLAST schemes.

关键词： algebraic code V-BLAST diversity list sphere decoder ML detection.

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Preventing a pitfall in trellis-based decoding of polynomial block codes

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ANNALES DES TELECOMMUNICATIONS-ANNALS OF TELECOMMUNICATIONS 2001年第9-10期56卷 505-509页

作者： Tortelier, P Berthet, A France Telecom R&D F-92131 Issy Les Moulineaux France

We give a simple proof of a well known property of the maximum likelihood decoding of polynomial block codes : the systematic version of the code results in fewer decoding errors than the non systematic version. As a practical result, it is interesting to decode the systematic version of the code on the treillis of the non systematic version, because the non systematic version of the code exhibits a more regular trellis, and both version generate the same codewords.

关键词： error correcting code Viterbi decoding block code treillis decoding algebraic code BCH code linear code

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