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Module minimisation based low-complexity soft decoding of Reed-Solomon codes

IET COMMUNICATIONS 2019年第20期13卷 3489-3499页

作者： Xing, Jiongyue Chen, Li Bossert, Martin Sun Yat Sen Univ Sch Elect & Informat Technol Guangzhou 510006 Peoples R China Ulm Univ Inst Commun Engn D-89073 Ulm Germany

The interpolation-based algebraic decoding for Reed-Solomon (RS) codes can correct errors beyond half of the code's minimum Hamming distance. Using soft information, the algebraic soft decoding (ASD) further improves the decoding performance. This paper presents a unified study of two classical ASD algorithms, the algebraic Chase decoding and the Koetter-Vardy decoding. Their computationally expensive interpolation is solved by the module minimisation (MM) technique which consists of basis construction and basis reduction. Compared with Koetter's interpolation, the MM interpolation yields a smaller computational cost for the two ASD algorithms. Re-encoding transform is further applied to reduce the decoding complexity by reducing the degree of module generators. Based on assessing the degree of module seeds, a complexity reducing approach is introduced to further facilitate the two ASD algorithms. Computational cost of the two algorithms as well as their re-encoding transformed variants will be analysed. Performance of the two ASD algorithms will be compared under decoding expenditure benchmark, providing more practical insights of their applications.

关键词： decoding Reed-Solomon codes computational complexity interpolation algebraic codes interpolation-based algebraic decoding Reed-Solomon codes soft information algebraic soft decoding decoding performance classical ASD algorithms algebraic Chase decoding Koetter-Vardy decoding computationally expensive interpolation module minimisation technique Koetter's interpolation MM interpolation yields decoding complexity module generators module seeds complexity reducing approach re-encoding transformed variants decoding expenditure benchmark low-complexity soft decoding

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Low-complexity Belief-Propagation decoding via Dynamic Silent-Variable-Node-Free Scheduling

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IEEE COMMUNICATIONS LETTERS 2017年第1期21卷 28-31页

作者： Aslam, Chaudhry Adnan Guan, Yong Liang Cai, Kui Han, Guojun Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Singapore Univ Technol & Design Dept Sci Singapore 487372 Singapore Guangdong Univ Technol Guangzhou 510006 Guangdong Peoples R China

This letter presents a low-complexity scheduling scheme, referred to as the dynamic silent-variable-node-free scheduling (D-SVNFS) scheme, for the sequential belief propagation decoding of LDPC code. The D-SVNFS regulates the dynamic propagation of message updates based on the checkto-variable message residuals. To determine the next message update, it computes the on-demand message residuals and selects the largest one associated with the last updated variable and check nodes. In addition, the D-SVNFS attempts to propagate more message updates toward the erroneous variable nodes, trying to correct them with higher priority. It is shown that the proposed scheduling reduces the BP decoding complexity by up to 70% compared with prior-art SVNF scheme, without affecting the error-rate performance, at medium to high signal-to-noise ratio over the BI-AWGN and Rayleigh fading channels.

关键词： LDPC codes belief-propagation dynamic scheduling decoding complexity error-rate performance

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Low-complexity decoding of Block Turbo Codes Based on the Chase Algorithm

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IEEE COMMUNICATIONS LETTERS 2017年第4期21卷 706-709页

作者： Son, Jaeyong Cheun, Kyungwhoon Yang, Kyeongcheol Pohang Univ Sci & Technol POSTECH Dept Elect Engn Pohang 37673 Gyeongbuk South Korea Samsung Elect Co Ltd Memory Business Controller Dev Team Suwon 16677 Gyeonggi South Korea Samsung Elect Co Ltd Mobile Commun Business Commun Res Grp Suwon 16677 Gyeonggi South Korea

Block turbo codes (BTCs) are constructed by serially concatenating linear block codes and iteratively decoded by letting each component code be decoded in two stages. The Chase algorithm is employed in the first stage to make a list of candidate codewords by generating a fixed number of test sequences (TSs) and algebraically decoding them, regardless of the signal-to-noise ratio or the iteration number. In the second stage, the extrinsic information is generated for iterative decoding. In this letter, we propose a low-complexity decoding algorithm for BTCs. The proposed algorithm first checks whether an algebraic hard-decision decoder outputs a codeword for a given decoder input vector, and then adaptively applies one of the two estimation rules. Based on these two rules, the number of TSs in the proposed algorithm can be made monotonically decreasing with iterations. Numerical results demonstrate that the proposed algorithm has much lower computational complexity with a negligible performance loss, compared with the conventional decoding scheme based on the Chase algorithm.

关键词： Adaptive decoding algorithm block turbo codes (BTCs) Chase algorithm decoding complexity

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Sequential decoding of Short Length Binary Codes: Performance Versus complexity

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IEEE COMMUNICATIONS LETTERS 2021年第10期25卷 3195-3198页

作者： Lian, Bo Kschischang, Frank R. Univ Toronto Edward S Rogers Sr Dept Elect & Comp Engn Toronto ON M5S 3G4 Canada

Sequential decoding of short length binary codes for the additive white Gaussian noise channel is considered. A variant of the variable-bias term (VBT) metric is introduced, producing useful trade-offs between performance and computational complexity. Comparisons are made with tail-biting convolutional codes decoded with a wrap-around Viterbi algorithm (WAVA) and with polar codes under successive-cancellation list (SCL) decoding. It is found that sequential decoding with the improved VBT metric has a better performance-complexity tradeoff than tail-biting codes under WAVA decoding (except at low complexities) but a worse performance-complexity tradeoff than polar codes under SCL decoding (except at high complexities).

关键词： decoding Measurement complexity theory Signal to noise ratio Maximum likelihood decoding Polar codes Convolutional codes decoding complexity short length codes sequential decoding stack algorithm variable bias-term metric polar codes

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Fast Successive-Cancellation decoding of 2 x 2 Kernel Non-Binary Polar Codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2025年第2期73卷 1009-1024页

作者： Farsiabi, Ali Ebrahimzad, Hamid Ardakani, Masoud Li, Chuandong Huawei Technol Co Ltd Ottawa ON K2K 3J1 Canada Univ Alberta Dept Elect & Comp Engn Edmonton AB T6G 2V4 Canada

Non-binary polar codes (NBPCs) decoded by successive cancellation (SC) algorithm have remarkable bit-error-rate performance compared to the binary polar codes (BPCs). Due to its serial nature, SC decoding suffers from long latency. The latency issue in BPCs has been the topic of extensive research and it has been notably resolved by the introduction of fast SC-based decoders. However, the latency problem of NBPCs is mainly untouched and the vast majority of research on NBPCs is devoted to issues concerning design and efficient implementation. In this paper, we propose fast SC decoding for NBPCs constructed based on 2 x 2 kernels. In particular, we extend the special nodes of BPCs to their non-binary counterpart and define various non-binary special nodes in the SC decoding tree of NBPCs and propose their fast decoding. This way, we avoid traversing the full decoding tree and significantly reduce the decoding delay compared to symbol-by-symbol SC decoding. We also propose a simplified NBPC structure that facilitates the procedure of non-binary fast SC decoding. Using our proposed fast non-binary decoder, we observe an improvement of more than 96% in latency concerning the original SC decoding. This is while our proposed fast SC decoder for NBPCs incurs no error-rate loss.

关键词： decoding Polar codes Vectors Symbols Kernel Forward error correction Parity check codes Non-binary polar code decoding latency fast non-binary polar decoder fast LNBSC decoder fast non-binary SC decoder decoding memory decoding complexity

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On the complexity of suboptimal decoding for list and decision feedback schemes

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DISCRETE APPLIED MATHEMATICS 2006年第2期154卷 294-304页

作者： Freudenberger, J Zyablov, V Univ Ulm Dept Telecommun & Appl Informat Theory D-89081 Ulm Germany Russian Acad Sci Inst Informat Transmiss Problems Moscow 101447 Russia

We consider bounded distance list decoding, such that the decoder calculates the list of all codewords within a sphere around the received vector. We analyze the performance and the complexity of this suboptimum list decoding scheme for the binary symmetric channel. The reliability function of the list decoding scheme is equivalent to the sphere-packing bound, where the decoding complexity is asymptotically bounded by 2(nR)(1-R). Furthermore, we investigate a decision feedback strategy that is based on bounded distance list decoding. Here, any output with zero or many codewords will call for a repeated transmission. In this case the decoding complexity will be of the order 2(nR)(1-C), where C denotes the channel capacity. The reliability function is close to Forney's feedback exponent. (c) 2005 Elsevier B.V. All rights reserved.

关键词： list decoding decision feedback bounded distance decoding error exponent decoding complexity

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Lowered-complexity decoding Algorithms of LDPC Codes for Agricultural-WSNs 11

Lowered-Complexity Decoding Algorithms of LDPC Codes for Agr...

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11th International Conference on Ubiquitous and Future Networks (ICUFN)

作者： Noh, Dong-Hee Jeong, Sung-Hwan Choi, Ju-Hwan Kim, Dong-Seong Korea Elect Technol Inst KETI Software Convergence Cluster Jeonju South Korea Kumoh Natl Inst Technol Dept IT Convergence Engn Gumi South Korea

ISBN: (纸本)9781728113395

This paper proposes a pattern based Low-density parity-check (LDPC) codes scheme to reduce the decoding complexity using logical XOR. New approaches to this paper describe the pattern based encoder which using logical XOR operation. The proposed scheme can reduce iteration, complexity and packet errors while decoding procedures. It can obtain enhanced throughput performance and at receiver sides in several Signal to Noise Ratio (SNR) levels. Simulation results show that the proposed method can improve the throughput and transmission delay for wireless sensor networks.

关键词： LDPC Sum Product Algorithm decoding decoding complexity decoding Throughput Wireless Sensor Network

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Linear Computational complexity decoding for Semi Orthogonal Full Rate Space Time Codes

Linear Computational Complexity Decoding for Semi Orthogonal...

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IEEE Wireless Communications and Networking Conference (WCNC)

作者： Laufer, Amir Bar-Ness, Yeheskel New Jersey Inst Technol Ctr Wireless Commun & Signal Proc Res ECE Newark NJ 07102 USA

ISBN: (纸本)9781612842547

Communication with low complexity decoding is an important attribute for many applications. From low cost, distributed sensors arrays with desirably long operative life to ultra smart handheld battery operated devices, low complexity decoding results in better power consumption and simpler hardware implementation. In this paper a linear decoding complexity is applied and analyzed to the semi-orthogonal space time codes which are rate 1 codes originated from a regular orthogonal space time codes. The proposed transmission and decoding schemes are very appealing in the sense that they improve the code rate of the orthogonal codes family, yet, maintain its simple, symbol by symbol decoding with no filter calculation complexity overhead. In addition, a performance boosting modifications are suggested and investigated for the basic transmission and decoding schemes under different system settings such as the availability of limited feedback and multiple receiving antennas.

关键词： Space time codes Full rate Diversity decoding complexity

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Low-complexity Chase decoding of Algebraic-Geometric Codes Using Koetter's Interpolation

Low-Complexity Chase Decoding of Algebraic-Geometric Codes U...

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IEEE Information Theory Workshop (ITW)

作者： Wu, Siyuan Chen, Li Johnston, Martin Sun Yat Sen Univ Sch Elect & Informat Technol Guangzhou 510006 Guangdong Peoples R China Newcastle Univ Sch Elect & Elect Engn Newcastle Upon Tyne NE1 7RU Tyne & Wear England

ISBN: (纸本)9781509010905

Algebraic-geometric (AG) codes have long been considered as a possible candidate to replace Reed-Solomon (RS) codes. However, their decoding remains complex and infeasible to implement. Addressing this challenge, our paper proposes a low-complexity Chase (LCC) decoding algorithm for the most popular class of AG codes - Hermitian codes. The LCC decoding is realised by formulating decoding test-vectors, which allows Koetter's interpolation to be performed for common and uncommon elements. This reduces redundant computations and also removes the need to calculate the corresponding coefficients of a Hermitian curve, thus facilitating message recovery. Our simulation results show that significant coding gains can be achieved over the conventional Koetter-Vardy (KV) soft decoding algorithm, but with a much lower computational cost. Moreover, we also show that in comparison with RS codes of a similar length, Chase decoding has a more significant impact on enhancing the performance of Hermitian codes.

关键词： Algebraic-geometric codes Chase decoding decoding complexity Hermitian codes interpolation

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Low complexity Iterative decoding Algorithm for Low-Density Parity-Check (LDPC) codes

Low Complexity Iterative Decoding Algorithm for Low-Density ...

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1st IFIP Wireless Days Conference

作者： Zeidan, Hany R. Elsabrouty, Maha M. Arab Acad Sci Technol & Maritime Transportat Fac Engn Dept Elect & Elect Commun Cairo Egypt

ISBN: (纸本)9781424428281

The reliability ratio weighted based bit-flipping (RRWBF) algorithm for decoding low-density parity-check (LDPC) codes has recently been developed to provide the best performance among all existing bit-flipping based algorithms. The implementation efficient reliability ratio weighted based bit-flipping (IERRWBF) algorithm speedup the original algorithm to decrease the processing time used. A drawback for this;algorithm is the decrease in the improvement as the maximum number of iterations assigned for the algorithm increase as a large percentage of decoding time is spent on the iteration part without any change in the performance. In this paper, a modified version for this algorithm is proposed to solve this drawback by reducing the number of iterations required to achieve the same performance of the existing IERRWBF algorithm using efficient number of iterations instead of using the maximum number of iterations for decoding without any change in the performance of the IERRWBF.

关键词： bit-flipping algorithm decoding complexity error sum low-density parity-check (LDPC) codes implementation efficient reliability ratio weighted bit-flipping (IERRWBF) algorithm

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