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list decoding of maximal order codes over number fields

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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A Universal list decoding Algorithm With Application to decoding of Polar Codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2025年第2期71卷 975-995页

作者： Zheng, Xiangping Ma, Xiao Sun Yat Sen Univ Sch Comp Sci & Engn Guangzhou 510006 Peoples R China Sun Yat Sen Univ Guangdong Key Lab Informat Secur Technol Guangzhou 510006 Peoples R China

This paper is concerned with a guessing codeword decoding (GCD) of linear block codes, which is optimal and typically requires a fewer number of searches than the naive exhaustive search decoding (ESD). Compared with the guessing random additive noise decoding (GRAND), which is only efficient for high-rate codes, the GCD is efficient for not only high-rate codes but also low-rate codes. We prove that the GCD typically requires a fewer number of queries than the GRAND. Compared with the conventional ordered statistics decoding (OSD), the GCD does not require the online Gaussian elimination (GE). In addition to limiting the maximum number of searches, we suggest limiting the radius of searches in terms of soft weights or tolerated performance loss to further reduce the decoding complexity, resulting in the so-called truncated GCD. The performance gap between the truncated GCD and the optimal decoding can be upper bounded approximately by the saddlepoint approach or other numerical approaches. The derived upper bound captures the relationship between the performance and the decoding parameters, enabling us to balance the performance and the complexity by optimizing the decoding parameters of the truncated GCD. We also introduce a parallel implementation of the (truncated) GCD algorithm to reduce decoding latency without compromising performance. Another contribution of this paper is the application of the GCD to the polar codes. We propose a multiple-bit-wise decoding algorithm over a pruned tree for the polar codes, referred to as the successive-cancellation list (SCL) decoding algorithm by GCD. First, we present a strategy for pruning the conventional polar decoding tree based on the complexity analysis rather than the specific bit patterns. Then we apply the GCD algorithm in parallel aided by the early stopping criteria to the leaves of the pruned tree. Simulation results show that, without any performance loss as justified by analysis, the proposed decoding algorit

关键词： Complexity theory Maximum likelihood decoding Codes Germanium Polar codes Vectors Ultra reliable low latency communication Reliability Generators Systematics Guessing codeword decoding (GCD) list decoding performance bound polar codes

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CRC-Aided High-Rate Convolutional Codes With Short Blocklengths for list decoding

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IEEE TRANSACTIONS ON COMMUNICATIONS 2024年第1期72卷 63-74页

作者： Sui, Wenhui Towell, Brendan Asmani, Ava Yang, Hengjie Grissett, Holden Wesel, Richard D. Univ Calif Los Angeles Dept Elect & Comp Engn Los Angeles CA 90095 USA Qualcomm Technol Inc San Diego CA 92121 USA

Recently, rate-1/n zero-terminated (ZT) and tail-biting (TB) convolutional codes (CCs) with cyclic redunancy check (CRC)-aided list decoding have been shown to closely approach the random-coding union (RU) bound for short blocklengths. This paper designs CRC polynomials for rate-(n-1)/nZT and TB CCs with short blocklengths. This paper considers both standard rate-(n-1)/nCC polynomials and rate-(n-1)/n designs resulting from puncturing a rate-1/2code. The CRC polynomials are chosen to maximize the minimum distanced d(min) and minimize the number of nearest neighbors A(dmin). For the standard rate-(n-1)/n codes, utilization of the dual trellis proposed by Yamada et al. lowers the complexity of CRC-aided serial list Viterbi decoding (SLVD).CRC-aided SLVD of the TBCCs closely approaches the RCU bound at a blocklength of128. This paper compares the FER performance (gap to the RCU bound) and complexity of the CRC-aided standard and punctured ZTCCs and TBCCs. This paper also explores the complexity-performance trade-off for three TBCC decoders: a single-trellis approach, a multi-trellis approach, and a modified single-trellis approach with pre-processing using the wrap around Viterbi algorithm.

关键词： Short blocklength convolutional codes (CCs) cyclic redundancy check codes list decoding

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Robust Video list decoding in Error-Prone Transmission Systems Using a Deep Learning Approach

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IEEE ACCESS 2024年 12卷 170632-170647页

作者： Zhang, Yujing Coulombe, Stephane Coudoux, Francois-Xavier Guichemerre, Alexis Corlay, Patrick Univ Quebec Ecole Technol Super Dept Software & IT Engn Montreal PQ H3C 1K3 Canada Univ Polytech Hauts de France Inst Elect Microelect & Nanotechnol IEMN Dept Optoacoustoelect DOAE CNRSUMR 8520 F-59313 Valenciennes France Univ Paris Saclay Int Lab Learning Syst ILLS McGill ETS Mila CNRS CentraleSupelec Montreal PQ H3H 2T2 Canada

This paper introduces a novel deep-learning assisted video list decoding method for error-prone video transmission systems. Unlike traditional list decoding techniques, our proposed system uses a Transformer-based no-reference image quality assessment method to select the highest-scoring reconstructed video candidate after reception. Three new components are defined and used in the Transformer-assisted image quality evaluation metric: neighborhood-based patch fidelity aggregation, discriminant color texture transformation and ranking-constrained penalty loss function. We have also created our own database of non-uniformly distorted images, similar to those that might result from transmission errors, in a High Efficiency Video Coding (HEVC) context. In our specific testing context, our improved Transformer-assisted method has a decision accuracy of 100% for intra-coded image, while, for errors occurring in an inter image, it is 96%. Notably, in the few cases where a wrong choice is made, the selected candidate's quality remains similar to the intact frame. Code: https://***/Yujing0926/Robust-Video-list-decoding-Using-a-Deep-Learning-Approach.

关键词： decoding Transformers Image quality Visualization Streaming media Distortion Reliability Error correction Streams Image reconstruction Video transmission list decoding non-uniform distortions no-reference image quality assessment vision transformer convolutional neural network

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On the Intersection of Multiple Insertion (or Deletion) Balls and its Application to list decoding Under the Reconstruction Model

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IEEE TRANSACTIONS ON INFORMATION THEORY 2024年第5期70卷 3262-3297页

作者： Abu-Sini, Maria Yaakobi, Eitan Technion Israel Inst Technol Dept Comp Sci IL-3200003 Haifa Israel

In the reconstruction model, first proposed by Levenshtein in 2001, a word is transmitted over multiple identical noisy channels that output distinct erroneous words. Given the channels' outputs, unique decoding of the transmitted word is guaranteed to succeed only if the number of the channels is greater than a specific value. Otherwise, there may be several transmitted words that lead to the same channels' outputs. In this case, these words are recovered using a list decoder. Calculating the largest list size is a fundamental task when studying the list decoding problem. The present work takes the first steps towards studying list decoding of insertions and deletions under the reconstruction model. More specifically, it assumes that an arbitrary binary word is transmitted over m t-insertion (or t-deletion) identical channels, and provides the largest list size for specific values of m. These results are mainly achieved by investigating the largest intersection of m t-insertion (or t-deletion) balls surrounding arbitrary binary words in the space.

关键词： Sequence reconstruction Levenshtein distance synchronization channels list decoding insertions deletions

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list decoding of Binary Subspace Chirps

List Decoding of Binary Subspace Chirps

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International Conference on Ubiquitous Communication (Ucom)

作者： Li, Pinmo Zheng, Jianping Xidian Univ Sch Telecommun Engn Xian 710071 Shaanxi Peoples R China

ISBN: (纸本)9798350374223;9798350374216

Binary subspace chirps (BSSCs) have been proposed recently which can provide a larger codebook and slightly better performance than the binary chirps (BCs) in the deterministic compressed sensing and random multiple access. A BSSC is characterized by a rank r, an on-off pattern part, and a BC part. In general, the rich algebra structure of BSSCs can be employed to design the low-complexity decoding algorithm. Here, to further improve the performance, we first study the breadth-first list decoding of BSSCs in the single-user scenario, with emphasis on the determination of the candidate list of the on-off pattern. Moreover, we extend it to the random access scenario where the multipath matching pursuit algorithm is utilized. Finally, the effectiveness of the proposed list decoder is demonstrated by computer simulations.

关键词： Binary subspace chirps compressed sensing breadth-first search list decoding random access

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Secure Codes With list decoding

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IEEE TRANSACTIONS ON INFORMATION THEORY 2024年第4期70卷 2430-2442页

作者： Gu, Yujie Vorobyev, Ilya Miao, Ying Kyushu Univ Fac Informat Sci & Elect Engn Fukuoka 8190395 Japan Tech Univ Munich Inst Commun Engn D-80333 Munich Germany Univ Tsukuba Fac Engn Informat & Syst Tsukuba Ibaraki 3058573 Japan

In this paper we consider combinatorial secure codes in traitor tracing for protecting copyright of multimedia content. First, we introduce a new notion of secure codes with list decoding (SCLDs) for collusion-resistant multimedia fingerprinting, which includes many existing types of fingerprinting codes as special cases. Next, we build efficient identifying algorithms for SCLDs with complete traceability and establish bounds on its largest possible code rate. In comparison with the existing fingerprinting codes, it is shown that SCLDs have not only much more efficient traceability than separable codes but also a much larger code rate than frameproof codes. As a byproduct, new bounds on the largest code rate of binary separable codes are established as well. Furthermore, a two-stage dynamic traitor tracing framework is proposed for multimedia fingerprinting in the dynamic scenario, which could not only efficiently achieve the complete traceability but also provide a much larger capacity than the static scenario.

关键词： Codes Fingerprint recognition decoding Data security Modulation Heuristic algorithms Streaming media Secure code list decoding dynamic traitor tracing copyright protection binary code code rate

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Probabilistic Shaping for Trellis-Coded Modulation With CRC-Aided list decoding

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IEEE TRANSACTIONS ON COMMUNICATIONS 2023年第3期71卷 1271-1283页

作者： Wang, Linfang Song, Dan Areces, Felipe Wiegart, Thomas Wesel, Richard D. Univ Calif Los Angeles Dept Elec & Comp Engn Los Angeles CA 90095 USA Stanford Univ Dept Elect Engn Stanford CA 94305 USA Tech Univ Munich TUM Inst Commun Engn D-80333 Munich Germany

This paper applies probabilistic amplitude shaping (PAS) to cyclic redundancy check (CRC)-aided tail-biting trellis-coded modulation (TCM). CRC-TCM-PAS produces practical codes for short block lengths on the additive white Gaussian noise (AWGN) channel. In the transmitter, equally likely message bits are encoded by a distribution matcher (DM) generating amplitude symbols with a desired distribution. A CRC is appended to the sequence of amplitude symbols, and this sequence is then encoded and modulated by TCM to produce real-valued channel input signals. This paper proves that the sign values produced by the TCM are asymptotically equally likely to be positive or negative. The CRC-TCM-PAS scheme can thus generate channel input symbols with a symmetric capacity-approaching probability mass function. The paper provides an analytical upper bound on the frame error rate of the CRC-TCM-PAS system over the AWGN channel. This FER upper bound is the objective function used for jointly optimizing the CRC and convolutional code. Additionally, this paper proposes a multi-composition DM, which is a collection of multiple constant-composition DMs. The optimized CRC-TCM-PAS systems achieve frame error rates below the random coding union (RCU) bound in AWGN and outperform the short-blocklength PAS systems with various other forward error correction codes studied in Coskun et al. (2019).

关键词： Reliable communication short blocklength probabilistic shaping trellis-coded modulation tail-biting convolutional code CRC list decoding distribution matcher

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IMPROVED list decoding OF FOLDED REED-SOLOMON AND MULTIPLICITY CODES

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SIAM JOURNAL ON COMPUTING 2023年第3期52卷 794-840页

作者： Kopparty, Swastik Ron-Zewi, Noga Saraf, Shubhangi Wootters, Mary Rutgers State Univ Dept Math Piscataway NJ 08854 USA Rutgers State Univ Dept Comp Sci Piscataway NJ 08854 USA Univ Haifa Dept Comp Sci IL-31905 Haifa Israel Stanford Univ Dept Comp Sci Stanford CA 94305 USA Stanford Univ Dept Elect Engn Stanford CA 94305 USA

We show new and improved list decoding properties of folded Reed-Solomon (RS) codes and multiplicity codes. Both of these families of codes are based on polynomials over finite fields, and both have been the source of recent advances in coding theory: folded RS codes were the first known explicit construction of capacity-achieving list decodable codes [V. Guruswami and A. Rudra, IEEE Trans. Inform. Theory, 54 (2008), pp. 135-150], and multiplicity codes were the first construction of high-rate locally decodable codes [S. Kopparty, S. Saraf, and S. Yekhanin, J. ACM, 61 (2014), 28]. In this work, we show that folded RS codes and multiplicity codes are in fact better than previously known in the context of list decoding and local list decoding. Our first main result shows that folded RS codes achieve list decoding capacity with constant list sizes, independent of the block length. Prior work with constant list sizes first obtained list sizes that are polynomial in the block length and relied on pre-encoding with subspace evasive sets to reduce the list sizes to a constant [V. Guruswami and C. Wang, IEEE Trans. Inform. Theory, 59 (2013), pp. 3257-3268], [Z. Dvir and S. Lovett, Proc. 44th STOC, ACM, 2012, 351-358]. The list size we obtain is (1/epsilon)(O)((1/epsilon)) where epsilon is the gap to capacity, which matches the list size obtained by pre-encoding with subspace evasive sets. For our second main result, we observe that univariate multiplicity codes exhibit similar behavior, and we use this, together with additional ideas, to show that multivariate multiplicity codes are locally list decodable up to their minimum distance. By known reductions, this gives, in turn, capacity-achieving locally list decodable codes with query complexity exp((& otilde;)((log N)(5)/(6))). This improves on the tensor-based construction of [B. Hemenway, N. Ron-Zewi, and M. Wootters, SIAM J. Comput., 49 (2019), pp. 157-195], which gave capacity-achieving locally list decodable codes of q

关键词： error-correcting codes list decoding local decoding folded Reed-Solomon codes multiplicity codes

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Belief Propagation list decoding for Polar Codes:Performance Analysis and Software Implementation on GPU

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China Communications 2023年第9期20卷 115-126页

作者： Zhanxian Liu Wei Li Lei Sun Wei Li Jianquan Wang Haijun Zhang School of Computer&Communication Engineering University of Science and Technology BeijingBeijing 100083China Satellite Frequency and Orbit Resource Agency State Radio Monitoring CenterBeijing 100041China School of Automation and Electrical Engineering University of Science and Technology BeijingBeijing 100083China Beijing Engineering and Technology Research Center for Convergence Networks and Ubiquitous Services Institute of Artificial IntelligenceUniversity of Science and Technology BeijingBeijing 100083China

Belief propagation(BP)decoding outputs soft information and can be naturally used in iterative *** list(BPL)decoding provides comparable error-correction performance to the successive cancellation list(SCL)*** this paper,we firstly introduce an enhanced code construction scheme for BPL decoding to improve its errorcorrection ***,a GPU-based BPL decoder with adoption of the new code construction is ***,the proposed BPL decoder is tested on NVIDIA RTX3070 and *** results show that the presented BPL decoder with early termination criterion achieves above 1 Gbps throughput on RTX3070 for the code(1024,512)with 32 lists under good channel conditions.

关键词： polar code belief propagation SIMT list decoding GPU

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