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A Fully Parallel LDPC Decoder Architecture Using Probabilistic min-sum algorithm for High-Throughput Applications

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2014年第9期61卷 2738-2746页

作者： Cheng, Chung-Chao Yang, Jeng-Da Lee, Huang-Chang Yang, Chia-Hsiang Ueng, Yeong-Luh Natl Tsing Hua Univ Dept Elect Engn Hsinchu Taiwan Natl Chiao Tung Univ Dept Elect Engn Hsinchu Taiwan Natl Tsing Hua Univ Inst Commun Engn Hsinchu Taiwan

This paper presents a normalized probabilistic min-sum algorithm for low-density parity-check (LDPC) codes, where a probabilistic second minimum value, instead of the true second minimum value, is used to facilitate fully parallel decoder realization. The comparators in each check-node unit (CNU) are connected through an interconnect network based on a mix of tree and butterfly networks such that the routing and message passing between the variable-node units (VNUs) and CNUs can be efficiently realized. In order to further reduce the hardware complexity, the normalization operation is realized in the VNU rather than in the CNU. An early termination scheme is proposed in order to prevent unnecessary energy dissipation for both low and high signal-to-noise-ratio regions. The proposed techniques are demonstrated by implementing a (2048, 1723) LDPC decoder using a 90 nm CMOS process. Post-layout simulation results show that the decoder supports a throughput of 45.42 Gbps at 199.6 MHz, achieving the highest throughput and throughput-to-area ratio among comparable works based on a similar or better error performance.

关键词： High-throughput decoder low-density parity-check (LDPC) codes min-sum algorithm

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Low-Complexity Parallel min-sum Medium-Density Parity-Check Decoder for McEliece Cryptosystem

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2023年第12期70卷 5328-5338页

作者： Cai, Jiaxuan Zhang, Xinmiao Ohio State Univ Dept Elect & Comp Engn Columbus OH 43210 USA

The McEliece cryptosystem based on medium-density parity-check (MDPC) codes remains a candidate in the fourth round submission of post-quantum cryptography standard. The low-density parity-check (LDPC) decoders used in digital communications have been extensively studied. However, the MDPC codes for the McEliece cryptosystem have much higher column weight and different structure in their parity-check matrices. As a result, simplification techniques for LDPC decoders are not applicable to MDPC decoders. Besides, existing MDPC decoder designs have been focusing on the simplest bit-flipping algorithm, whose performance is inferior compared to that of the min-sum algorithm. This paper first optimizes the scaled min-sum algorithm for codes with high column weight to improve the performance with simple scalar multiplications. The overall decoder architecture is re-designed to take into account the sparsity of the parity-check matrix and nontrivial min-sum check node processing. Besides, a flexible message storage scheme is proposed to reduce the worst-case decoding latency of the randomly constructed codes utilized in the McEliece cryptosystem. Then a 2-stage scaling scheme is developed to reduce the long critical path caused by the high column weight and a group size re-balancing scheme is introduced to mitigate the precision loss caused by the 2-stage scaling in parallel decoders. For an example MDPC decoder, the proposed optimized 2-stage scaled min-sum algorithm leads to orders of magnitude error-correcting performance improvement and 16% higher clock frequency with negligible silicon area overhead compared to unoptimized min-sum decoders.

关键词： McEliece cryptosystem error-correcting codes medium-density parity-check codes min-sum algorithm parallel decoder post-quantum cryptography

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Low-Latency Parallel Row-Layered min-sum MDPC Decoder for McEliece Cryptosystem 37

Low-Latency Parallel Row-Layered Min-sum MDPC Decoder for Mc...

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2024 International Workshop on Signal Processing Systems

作者： Cai, Jiaxuan Zhang, Xinmiao Ohio State Univ Dept Elect & Comp Engn Columbus OH 43210 USA

ISBN: (纸本)9798350373769;9798350373752

In the latest round of post-quantum cryptography standardization, the McEliece cryptosystem utilizing medium-density parity-check (MDPC) codes remains a candidate. The row-layered min-sum decoding for MDPC codes has better trade-off between performance and complexity. Previous work adds constraints to the parity-check matrix construction in order to enable efficient parallel decoding. However, the constraints for large parallelism cause an undesirable reduction in the number of usable secret keys and hence the previous scheme has limitations in achieving higher speed. This paper proposes two new schemes to substantially reduce the latency of row-layered MDPC decoding. Instead of further increasing the constraints to achieve higher parallelism, multiple identity blocks in the parity-check matrix are processed simultaneously in the first scheme and large blocks of variable width are processed in a hybrid way in the second design. Efficient hardware architectures are also developed for both proposed decoders. For an example code, the two proposed decoders achieve around 40% speedup compared to the best prior effort with less than 10% area overhead.

关键词： Error-correcting codes McEliece cryptosystem medium-density parity-check codes min-sum algorithm parallel decoder post-quantum cryptography row-layered scheduling

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Channel Coding Toward 6G: Technical Overview and Outlook

IEEE OPEN JOURNAL OF THE COMMUNICATIONS SOCIETY

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IEEE OPEN JOURNAL OF THE COMMUNICATIONS SOCIETY 2024年 5卷 2585-2685页

作者： Rowshan, Mohammad Qiu, min Xie, Yixuan Gu, Xinyi Yuan, Jinhong Univ New South Wales Sch Elect Engn & Telecommun Sydney NSW 2052 Australia

Channel coding plays a pivotal role in ensuring reliable communication over wireless channels. With the growing need for ultra-reliable communication in emerging wireless use cases, the significance of channel coding has amplified. Furthermore, minimizing decoding latency is crucial for critical-mission applications, while optimizing energy efficiency is paramount for mobile and the Internet of Things (IoT) communications. As the fifth generation (5G) of mobile communications is currently in operation and 5G-advanced is on the horizon, the objective of this paper is to assess prominent channel coding schemes in the context of recent advancements and the anticipated requirements for the sixth generation (6G). In this paper, after considering the potential impact of channel coding on key performance indicators (KPIs) of wireless networks, we review the evolution of mobile communication standards and the organizations involved in the standardization, from the first generation (1G) to the current 5G, highlighting the technologies integral to achieving targeted KPIs such as reliability, data rate, latency, energy efficiency, spectral efficiency, connection density, and traffic capacity. Following this, we delve into the anticipated requirements for potential use cases in 6G. The subsequent sections of the paper focus on a comprehensive review of three primary coding schemes utilized in past generations and their recent advancements: low-density parity-check (LDPC) codes, turbo codes (including convolutional codes), and polar codes (alongside Reed-Muller codes). Additionally, we examine alternative coding schemes like Fountain codes (also known as rate-less codes), sparse regression codes, among others. Our evaluation includes a comparative analysis of error correction performance and the performance of hardware implementation for these coding schemes, providing insights into their potential and suitability for the upcoming 6G era. Lastly, we will briefly explore consider

关键词： Codes 5G mobile communication 3GPP 6G mobile communication Reliability Iterative decoding 3G mobile communication Channel coding error control coding error correction codes wireless mobile communications 5th generation 5G 6th generation 6G encoding decoding channel polarization polar codes PAD codes monomial codes CRC low-density parity-check codes LDPC codes convolutional codes turbo codes spatially coupled codes fountain codes spinal codes raptor codes Luby transform codes LT codes lattice codes nonbinary codes sparse regression codes SPARC machine learning neural codes neural decoding successive cancellation decoding beleif propagation decoing Message Passing Decoding BCJR decoding iterative decoding Viterbi decoding Fano decoding automorphism ensemble decoding min-sum algorithm bit-flipping PPV bound normal approximation coded modulation bit-interleaving puncturing shortening repetition ratecompatible codes application layer channel coding physical layer waveform non-terrestrial networks free space optical links modulation block error rate BLER frame error rate FER reliability latency complexity enhanced mobile broadband eMBB machine-type communications MTC ultra-reliable low-latency URLLC key performance indicator KPI hardware architecture waveform design

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A review of channel coding schemes in the 5G standard

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TELECOMMUNICATION SYSTEMS 2023年第4期83卷 423-448页

作者： Kumar, Navin Kedia, Deepak Purohit, Gaurav GJUS&T Dept ECE Hisar Haryana India CSIR CEERI Adv Intelligent Technol Grp Pilani Rajasthan India

The channel in a communication system is usually affected by noise, so channel coding is employed to avoid contamination of data due to noise. Channel coding is a significant and persuasive part of cellular communication systems, which increases the reliability of data transmission by detecting and correcting errors generated in the data while passing through the channel. The fourth generation standard can't achieve desired channel capacity and latency due to its high error floor, which is a challenge. For fifth generation (5G), two different channel coding techniques have been chosen by third generation partnership project for error-free data transmission. In the 5G standard, the data and control channels use low-density parity check (LDPC) and polar codes, respectively, due to their inherent benefits. This paper broadly surveys channel coding techniques varying code rate (R), codeword (N) and message (K) bits for encoding and list size (L) and iterations in decoding for 5G standards. The MATLAB-based simulation helps to find the best channel for the 5G standard considering the bit error rate (BER) and channel capacity performance among additive white Gaussian noise (AWGN), Rayleigh and Rician channels for different channel coding and modulation techniques. The Monte-Carlo simulation shows that the LDPC codes with higher iteration and polar codes with larger list sizes achieve better BER performance keeping the code rate and modulation order lower for the AWGN channel. The simulation findings demonstrate that the distributed cyclic redundancy check successive cancellation list polar decoder outperforms the LDPC min-sum decoder without offset (N = 1024, K = 512, iteration or L = 16) but with offset it enhances LDPC's BER performance making it suitable for even shorter N.

关键词： Polar codes LDPC codes Non-systematic polar encoder Systematic polar encoder min-sum algorithm Successive cancellation list decoding

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High Throughput and Hardware Efficient Hybrid LDPC Decoder Using Bit-Serial Stochastic Updating

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2023年第9期70卷 3653-3664页

作者： Hu, Shuai Han, Kaining Zhu, Yubin Shen, Guodong Wang, Fujie Hu, Jianhao Univ Elect Sci & Technol China Natl Key Lab Sci & Technol Commun Chengdu 610054 Peoples R China

Hybrid low-density parity-check (LDPC) decoding combines conventional Belief-Propagation (BP) algorithm with stochastic decoding to achieve high performance and low complexity simultaneously. However, lossy and inefficient stochastic to-binary (S2B) conversion brings extra performance degradation and decoding latency. In this paper, a bit-serial stochastic updating based hybrid decoding (BSSU-HD) is proposed, which employs fully correlated stochastic (FCS) check nodes (CNs) and probability tracers assisted variable nodes (VNs) to accomplish accurate and efficient S2B conversion. Two strategies, including random source selection and tracing speed switching, are proposed to further improve performance and convergence. A BSSU LDPC decoder for IEEE 802.3an is designed in a 65-nm CMOS process, which occupies 4.6 mm(2) silicon area and achieves a throughput of 200.8 Gb/s at E-b/N-0 = 4.4 dB with 500 MHz clock frequency from a 1.2 V supply voltage. The power and energy efficiency are 2.933 W and 14.61 pJ/bit, respectively. To the best of our known, it achieves the best decoding performance, the highest throughput and hardware efficiency among state-of-the-art IEEE 802.3an LDPC decoders. We also verify that the BSSU-HD can achieve better performance for multi-rate 5th generation (5G) New Ratio (NR) LDPC codes than conventional algorithm, which greatly extends the application of the stochastic decoding.

关键词： Decoding Iterative decoding Hardware Throughput IEEE 802 3 Standard EPON Stochastic processes LDPC code probability tracer fully correlated stochastic min-sum algorithm

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A Distributed Approach for Robotic Coverage Path Planning Under Steep Slope Terrain Conditions

A Distributed Approach for Robotic Coverage Path Planning Un...

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IEEE Symposium Series on Computational Intelligence (IEEE SSCI)

作者： Martinez-Figueora, Dania Das, Sanjoy Badgujar, Chetan Flippo, Daniel Welch, Stephen J. Kansas State Univ Dept Elect & Comp Engn Manhattan KS 66505 USA Kansas State Univ Dept Biol & Agr Engn Manhattan KS 66505 USA Kansas State Univ Div Agron Manhattan KS 66506 USA

ISBN: (纸本)9781665487689

This article proposes a novel algorithm to determine the optimal coverage path of a mobile robot for uniform seed dispersion in any tract of agricultural land. The robot is required to operate under steep terrain conditions that are too risky for conventional, human operated equipment. Using data from an field experiment with the real robot, machine learning based function approximators are trained to estimate the minimum energy paths between adjacent points. Exemplar-based clustering is used to identify a suitable subset of way-points that ensure full coverage of a tract of land. An optimal cyclic tour is computed from the way points using a new asymmetric TSP algorithm proposed for this specific application. The clustering and the cyclic path planning algorithms can be implemented entirely through local message passing in a field-deployed sensor network. Simulations with synthetic as well as real topographic data establish the overall effectiveness of the proposed method.

关键词： Affinity propagation agricultural robot exemplar clustering message passing min-sum algorithm mobile robot traveling salesperson problem path planning

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NOLD: A Neural-Network Optimized Low-Resolution Decoder for LDPC Codes

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JOURNAL OF COMMUNICATIONS AND NETWORKS 2021年第3期23卷 159-170页

作者： Chu, Lei He, Huanyu Pei, Ling Qiu, Robert C. Shanghai Jiao Tong Univ Sch Elect Informat & Elect Engn Shanghai 200240 Peoples R China

The min-sum (MS) algorithm can decode Low-density parity-check (LDPC) codes with low computational complexity at the cost of slight performance loss. It is an effective way to realize hardware implementation of the min-sum decoder by quantizing the floating belief messages (i.e., check-to-variable messages and variable-to-check messages) into low-resolution (i.e., 2-4 bits) versions. However, such a way can lead to severe performance degradation due to the finite precision effect. In this paper, we propose a neural-network optimized low-resolution decoding (NOLD) algorithm for LDPC codes to deal with the problem. Specifically, the optimization of decoding parameters (i.e., scaling factors and quantization step) is achieved in a hybrid way, in which we concatenate a NOLD decoder with a customized neural network. All learnable parameters associated with the decoding parameters are assigned to each neuron in the proposed method. What's more, we design a new activation function whose outputs are close to the employed quantizer ones when network parameters are finally optimized off-line. Finally, the performance of the proposed method is verified by numerous experiments. For the case of 2-bit decoding, the proposed approach significantly outperforms several conventional decoders at the expense of slightly increased off-line training time. Besides, the proposed method with 4-bit quantization incurs only 0.1 dB performance loss compared with the floating min-sum decoder at the coded bit-error-rate of 10(-5). Moreover, we show that the proposed NOLD decoder works over a wide range of channel conditions for regular and irregular LDPC codes. Simulation code for reproductive results is publicly available(1).

关键词： Low-density parity-check codes low-resolution min-sum algorithm neural network optimization

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Convergence Properties of Message-Passing algorithm for Distributed Convex Optimisation With Scaled Diagonal Dominance

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2021年 69卷 3868-3877页

作者： Zhang, Zhaorong Fu, minyue Univ Newcastle Sch Elect Engn & Comp Univ Dr Callaghan NSW 2308 Australia

This paper studies the convergence properties of the well-known message-passing algorithm for convex optimisation. Under the assumption of pairwise separability and scaled diagonal dominance, asymptotic convergence is established and a simple bound for the convergence rate is provided for message-passing. In comparison with previous results, our results do not require the given convex program to have known convex pairwise components and that our bound for the convergence rate is tighter and simpler. When specialised to quadratic optimisation, we generalise known results by providing a very simple bound for the convergence rate.

关键词： Convergence Optimization Signal processing algorithms Linear programming Couplings Belief propagation Task analysis Distributed optimisation message passing belief propagation min-sum algorithm convex optimisation

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A Low-Complexity Decoder With Non-Uniform Quantization for Recursive BMST Codes

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IEEE COMMUNICATIONS LETTERS 2021年第8期25卷 2463-2467页

作者： Ai, Shengbo Zhao, Shancheng Jinan Univ Coll Informat Sci & Technol Guangzhou 510632 Peoples R China Guangdong Key Lab Data Secur & Privacy Preserving Guangzhou 510632 Peoples R China

Recursive block Markov superposition transmission (rBMST) can be used to construct high-performance spatially coupled codes. When used in power-limited scenarios, low-complexity quantized decoders are required for the rBMST codes. In this letter, we introduce an efficient decoder for rBMST codes by incorporating non-uniform quantization (NUQ) into the threshold attenuated min-sum algorithm (TAMSA). The resulting decoder is referred to as the NUQ-TAMSA. We use the hierarchical dynamic quantization algorithm to design the non-uniform quantizer. To show the effectiveness of the NUQ-TAMSA, we carry out comprehensive comparisons. Our results show that, for low-resolution quantization, performance gains as large as 0.3 dB can be obtained with the NUQ-TAMSA. Numerical results also show that, for a wide range of coding rates, 5-bits non-uniform quantization is sufficient for NUQ-TAMSA to approach the performances of the floating-point based TAMSA.

关键词： Decoding Quantization (signal) Encoding Heuristic algorithms Complexity theory Iterative decoding Mutual information Low complexity decoding min-sum algorithm non-uniform quantization recursive block Markov superposition transmission (BMST) codes

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