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Base Field Extension of AG Codes for decoding

IEEE TRANSACTIONS ON INFORMATION THEORY 2022年第6期68卷 3740-3743页

作者： Lee, Kwankyu Chosun Univ Dept Math Educ Gwangju 61452 South Korea

Previous algorithms for decoding AG codes up to the designed distance all assumed existence of an extra rational place on the base algebraic curve. The place is used to solve the decoding problem by linear algebra over the base field of the curve. The rationality of the place is essential, and therefore AG codes supported by all rational places on the curve are excluded from the domain of applicability of the decoding algorithms. This paper presents a decoding algorithm for those AG codes using an extra place of higher degree. Hence finally all AG codes, as Goppa defined 40 years ago, are equipped with a fast decoding algorithm.

关键词： decoding Codes Linear codes Geometry Generators Tensors Standards Algebraic geometry code decoding algorithm

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Sentence-level heuristic tree search for long text generation

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COMPLEX & INTELLIGENT SYSTEMS 2024年第2期10卷 3153-3167页

作者： Chen, Zheng Liu, Zhejun Univ Elect Sci & Technol China Sch Informat & Software Engn 4 Sect 2 North Jianshe Rd Chengdu 610054 Sichuan Peoples R China

In this study, we primarily aim to address the exposure bias issue in long text generation intrinsic to statistical language models. We propose a sentence-level heuristic tree search algorithm, specially tailored for long text generation, to mitigate the problem by managing generated texts in a tree structure and curbing the compounding of biases. Our algorithm utilizes two pre-trained language models, an auto-regressive model for generating new sentences and an auto-encoder model for evaluating sentence quality. These models work in tandem to perform four critical operations: expanding the text tree with new sentences, evaluating the quality of the additions, sampling potential unfinished text fragments for further generation, and pruning leaf nodes deemed unpromising. This iterative process continues until a pre-defined number of [EOS] tokens are produced, at which point we select the highest-scoring completed text as our final output. Moreover, we pioneer two novel token-level decoding techniques-nucleus sampling with temperature and diverse beam search with sampling. These methods, integrated with our sentence-level search algorithm, aim to improve the consistency and diversity of text generation. Experimental results, both automated measures (including Jaccard similarity, Word2vec similarity, and unique word ratio) and human evaluations (assessing consistency, fluency, and rhetorical skills), conclusively demonstrate that our approach considerably enhances the quality of machine-generated long-form text. Through this research, we aim to inspire further innovations in sentence-level search-based text generation algorithms.

关键词： Text generation Heuristic search decoding algorithm

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Skew differential Goppa codes and their application to Mceliece cryptosystem

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DESIGNS CODES AND CRYPTOGRAPHY 2023年第12期91卷 3995-4017页

作者： Gomez-Torrecillas, Jose Lobillo, F. J. Navarro, Gabriel Univ Granada Dept Algebra Ave Fuentenueva S-N Granada 18071 Spain Univ Granada Dept Comp Sci & Artificial Intelligence Periodista Daniel Saucedo Aranda S-N Granada 18071 Spain Univ Granada IMAG Ventanilla 11 Granada 18001 Spain Univ Granada CITIC Periodista Rafael Gomez Montero 2 Granada 18071 Spain

A class of linear codes that extends classical Goppa codes to a non-commutative context is defined. An efficient decoding algorithm, based on the solution of a non-commutative key equation, is designed. We show how the parameters of these codes, when the alphabet is a finite field, may be adjusted to propose a McEliece-type cryptosystem.

关键词： Skew-differential Goppa code decoding algorithm McEliece-type cryptosystem

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Improved BP decoding algorithm for LDPC Codes

Improved BP Decoding Algorithm for LDPC Codes

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International Conference on Mechatronics and Semiconductor Materials (ICMSCM 2013)

作者： Wang, Lina Liu, Xiao Univ Sci & Technol Beijing Dept Commun Engn Sch Comp & Commun Engn Beijing 100083 Peoples R China

ISBN: (纸本)9783037859391

In this paper, an improved belief propagation decoding algorithm was proposed for low density parity check codes. In the proposed decoding process, error bits can be detected once again after hard-decision in the conventional BP decoding algorithm. The detection criterion is based on check matrix characteristics and D-value between prior probability and posterior probability. Simulation results demonstrate the performance of the improved BP decoding algorithm outperform that of the conventional BP decoding algorithm.

关键词： low density parity check codes belief propagation decoding algorithm

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A Reduced Latency List decoding algorithm for Polar Codes

A Reduced Latency List Decoding Algorithm for Polar Codes

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IEEE Workshop on Signal Processing Systems (SiPS)

作者： Lin, Jun Xiong, Chenrong Yan, Zhiyuan Lehigh Univ Dept Elect & Comp Engn Bethlehem PA 18015 USA

ISBN: (纸本)9781479965885

The cyclic redundancy check (CRC) aided successive cancelation list (SCL) decoding algorithm has better error performance than the successive cancelation (SC) decoding algorithm for short or moderate polar codes. However, the CRC aided SCL (CA-SCL) decoding algorithm still suffer from long decoding latency. In this paper, a reduced latency list decoding (RLLD) algorithm for polar codes is proposed. For the proposed RLLD algorithm, all rate-0 nodes and part of rate-1 nodes are decoded instantly without traversing the corresponding subtree. A list maximum-likelihood decoding (LMLD) algorithm is proposed to decode the maximum likelihood (ML) nodes and the remaining rate-1 nodes. Moreover, a simplified LMLD (SLMLD) algorithm is also proposed to reduce the computational complexity of the LMLD algorithm. Suppose a partial parallel list decoder architecture with list size L = 4 is used, for an (8192, 4096) polar code, the proposed RLLD algorithm can reduce the number of decoding clock cycles and decoding latency by 6.97 and 6.77 times, respectively.

关键词： Government Polar code Government error performance decoding list decoding clock cycle Latency decoding algorithm Ganglia complexity classes

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A Novel HMM decoding algorithm Permitting Long-Term Dependencies and its Application to Handwritten Word Recognition 14

A Novel HMM Decoding Algorithm Permitting Long-Term Dependen...

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14th International Conference on Frontiers in Handwriting Recognition (ICFHR)

作者： Frinken, Volkmar Kakisako, Ryosuke Uchida, Seiichi Kyushu Univ Fac Informat Sci & Elect Engn Fukuoka 812 Japan

ISBN: (纸本)9781479943357

A new decoding for hidden Markov models is presented. As opposed to the commonly used Viterbi algorithm, it is based on the Min-CuUMax-Flow algorithm instead of dynamic programming. Therefore non-Markovian long-term dependencies can easily be added to influence the decoding path while still finding the optimal decoding in polynomial time. We demonstrate through an experimental evaluation how these constraints can be used to improve an HMM-based handwritten word recognition system that model words via linear character-HMM by restricting the length of each character.

关键词： Character recognition decoding Handwriting recognition Heuristic algorithms Hidden Markov models Training Viterbi algorithm Hidden Markov models Viterbi algorithm handwriting recognition decoding Character recognition Heuristic algorithms Functional training word recognition decoding algorithm

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Byzantine-Robust Private Information Retrieval with Low Communication and Efficient decoding 22

Byzantine-Robust Private Information Retrieval with Low Comm...

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17th ACM ASIA Conference on Computer and Communications Security 2022 (ACM ASIACCS)

作者： Zhang, Liang Feng Wang, Huaxiong Wang, Li-Ping ShanghaiTech Univ Sch Informat Sci & Technol Shanghai Peoples R China Nanyang Technol Univ Sch Phys & Math Sci Singapore Singapore Chinese Acad Sci Inst Informat Engn Beijing Peoples R China

ISBN: (纸本)9781450391405

A b Byzantine-robust K-out-of-l private information retrieval ((b,K, l)-BRPIR) scheme allows a user to retrieve any item of a database from l servers, even if only K out of the l servers respond and at most b out of the K responding servers provide false answers. The existing BRPIR schemes require either an exponential time decoding algorithm or a communication complexity no better than O (n(1/(2k-1))kl log l) with k = K-2b In this paper, we show a new (b, K, l)-BRPIR scheme that has both a polynomial time decoding algorithm and a communication cost of l . exp(O ((log n)(1-1/r) (log log n)(1/r))) for r = log(K /(2b + 1)), which is more efficient when n -> infinity.

关键词： private information retrieval matching vector codes byzantine-robust communication complexity decoding algorithm

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A Dynamic Hybrid Decoder Apprroach Using EG-LDPC Codes for Signal Processing Applications

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WIRELESS PERSONAL COMMUNICATIONS 2022年第2期122卷 1435-1454页

作者： Babu, J. Chinna Rao, Nuka Mallikharjuna Ramana, Kadiyala Bhaskar, Vidhyacharan Annamacharya Inst Technol & Sci Dept Elect & Commun Engn Rajampet Andhra Pradesh India Annamacharya Inst Technol & Sci Dept Comp Sci & Engn Rajampet Andhra Pradesh India San Francisco State Univ Dept Elect & Comp Engn San Francisco CA 94132 USA

The Low-Density Parity Check (LDPC) codes of Euclidean Geometry (EG) are encrypted and decrypted in numerous ways, namely Soft Bit Flipping (SBF), Sequential Peeling Decoder (SPD), Belief Propagation Decoder (BPD), Majority Logic Decoder/Detector (MLDD), and Parallel Peeling Decoder (PPD) decoding algorithms. These algorithms provide aextensive range of trade-offs between latency decoding, power consumption, hardware complexity-required resources, and error rate performance. Therefore, the problem is to communicate a sophisticated technique specifying the both soft and burst errors for effective information transmission. In this research, projected a technique named as Hybrid SBF (HSBF) decoder for EG-LDPC codes, which reduces the decoding complexity and maximizes the signal transmission and reception. In this paper, HSBF is also known as Self Reliability based Weighted Soft Bit Flipping (SRWSBF) Decoder. It is obvious from the outcomes that the proposed technique is better than the decoding algorithms SBF, MLDD, BPD, SPD and PPD. Using Xilinx synthesis and SPARTAN 3e, a simulation model is designed to investigate latency, hardware utilization and power consumption. Average latency of 16.65 percent is found to be reduced. It is observed that in considered synthesis parameters such as number of 4-input LUTs, number of slices, and number of bonded IOBs, excluding number of slice Flip-Flops, hardware utilization is minimized to an average of 4.25 percent. The number of slices Flip-Flops resource use in the proposed HSBF decoding algorithm is slightly higher than other decoding algorithms, i.e. 1.85%. It is noted that, over the decoding algorithms considered in this study, the proposed research study minimizes power consumption by an average of 41.68%. These algorithms are used in multimedia applications, processing systems for security and information.

关键词： Low Density Parity Check (LDPC) EG-LDPC Soft errors Burst errors decoding algorithm HSBF (SRWSBF) Multimedia applications Security

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Construction and Encoding algorithm for Maximum Run-Length Limited Single Insertion/Deletion Correcting Code

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2022年第1期E105A卷 35-43页

作者： Takemoto, Reona Nozaki, Takayuki Yamaguchi Univ Div Fundamental Sci Grad Sch Sci & Technol Innovat Dept Informat Yamaguchi 7538512 Japan Yamaguchi Univ Res Inst Time Studies Yamaguchi 7538511 Japan

Maximum run-length limited codes are constraint codes used in communication and data storage systems. Insertion/deletion correcting codes correct insertion or deletion errors caused in transmitted sequences and are used for combating synchronization errors. This paper investigates the maximum run-length limited single insertion/deletion correcting (RLL-SIDC) codes. More precisely, we construct efficiently encodable and decodable RLL-SIDC codes. Moreover, we present its encoding and decoding algorithms and show the redundancy of the code.

关键词： single insertion/deletion correcting codes maximum run-length limited codes encoding algorithm decoding algorithm

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An Efficient Decoder for a Linear Distance Quantum LDPC Code 2023

An Efficient Decoder for a Linear Distance Quantum LDPC Code

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55th Annual ACM Symposium on Theory of Computing (STOC) part of the ACM Federated Computing Research Conference (FCRC)

作者： Gu, Shouzhen Pattison, Christopher A. Tang, Eugene CALTECH Inst Quantum Informat & Matter Pasadena CA 91125 USA MIT Ctr Theoret Phys Cambridge MA USA

ISBN: (纸本)9781450399135

Recent developments have shown the existence of quantum low-density parity check (qLDPC) codes with constant rate and linear distance. A natural question concerns the efficient decodability of these codes. In this paper, we present a linear time decoder for the recent quantum Tanner codes construction of asymptotically good qLDPC codes, which can correct all errors of weight up to a constant fraction of the blocklength. Our decoder is an iterative algorithm which searches for corrections within constant-sized regions. At each step, the corrections are found by reducing a locally defined and efficiently computable cost function which serves as a proxy for the weight of the remaining error.

关键词： Quantum error correction quantum low-density parity-check codes decoding algorithm expander graphs robust error-correcting codes

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