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Deep Learning-Based Decoding of linear block codes for Spin-Torque Transfer Magnetic Random Access Memory

IEEE TRANSACTIONS ON MAGNETICS 2021年第2期57卷

作者： Zhong, Xingwei Cai, Kui Mei, Zhen Quek, Tony Q. S. Singapore Univ Technol & Design SUTD Singapore 487372 Singapore Huawei Technol Co Ltd Shenzhen 518129 Peoples R China

Thanks to its superior features of fast read/write speed and low power consumption, spin-torque transfer magnetic random access memory (STT-MRAM) has become a promising non-volatile memory (NVM) technology that is suitable for many applications. However, the reliability of STT-MRAM is seriously affected by the variation of the memory fabrication process and the working temperature, and the later will lead to an unknown offset of the channel. Hence, there is a pressing need to develop more effective error correction coding techniques to tackle these imperfections and improve the reliability of STT-MRAM. In this work, we propose, for the first time, the application of deep-learning (DL)-based algorithms and techniques to improve the decoding performance of linear block codes with short codeword lengths for SIT-MRAM. We formulate the belief propagation (BP) decoding of linear block code as a neural network (NN) and propose a novel neural normalized-offset reliability-based min-sum (RB-MS) (NNORB-MS) decoding algorithm. We successfully apply our proposed decoding algorithm to the STT-MRAM channel through channel symmetrization to overcome the channel asymmetry. We also propose an NN-based soft information generation method (SIGM) to take into account the unknown offset of the channel. Simulation results demonstrate that our proposed NNORB-MS decoding algorithm can achieve significant performance gain over both the hard-decision decoding (HDD) and the regular RB-MS decoding algorithm, for cases without and with the unknown channel offset. Moreover, the decoder structure and time complexity of the NNORB-MS algorithm remain similar to those of the regular RB-MS algorithm.

关键词： Deep learning (DL) linear block code reliable-based min-sum (RB-MS) decoding spin-torque transfer magnetic random access memory (STT-MRAM)

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The optimal sectionalized trellises for the generalized version of Viterbi algorithm of linear block codes and its application to Reed-Muller codes

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2000年第11期E83A卷 2329-2340页

作者： Tang, YS Fujiwara, T Kasami, T Osaka Univ Grad Sch Engn Sci Dept Informat & Math Sci Toyonaka Osaka 5608531 Japan Hiroshima City Univ Fac Informat Sci Dept Comp Sci Hiroshima 7313194 Japan

An algorithim for finding the optimal sectionalization for sectionalized trellises with respect to distinct optimality criterions was presented by Lafourcade and Vardy. In this paper, for linear block codes, we give a direct method for finding the optimal sectionalization when the optimality criterion is chosen as the total number \E\ of the edges, the expansion index \E\ - \V\ + 1, or the quantity 2\E\ - \V\ + 1, only using the dimensions of the past and Future sub-codes. A more concrete method For determining the optimal sectionalization is given for the Reed-Muller codes with the natural lexicographic coordinate ordering.

关键词： linear block code sectionalization minimal sectionalized trellis generalized Viterbi algorithm computational complexity

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Matrix embedding in steganography with binary Reed-Muller codes

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IET IMAGE PROCESSING 2017年第7期11卷 522-529页

作者： Yang, Tingya Chen, Houshou Natl Chung Hsing Univ Dept Elect Engn Taichung 402 Taiwan Natl Chung Hsing Univ Grad Inst Commun Engn Taichung 402 Taiwan

This study presents a modified majority-logic decoding algorithm of Reed-Muller (RM) codes for matrix embedding (ME) in steganography. An ME algorithm uses linear block code to improve the embedding efficiency in steganography. The optimal embedding algorithm in steganography is equivalent to the maximum likelihood decoding (MLD) algorithm in error-correcting codes. The main disadvantage of ME is that the equivalent MLD algorithm of lengthy embedding codes requires highly complex embedding. This study used RM codes to embed data in binary host images. The authors propose a novel low-complexity embedding algorithm that uses a modified majority-logic algorithm to decode RM codes, in which a message-passing algorithm (i.e. sum-product, min-sum, or bias propagation) is performed on the highest order of information bits in the RM codes. The experimental results indicate that integrating bias propagation into the proposed scheme achieves superior embedding efficiency (relative to when the sum-product or min-sum algorithm is used) and can even achieve the embedding bound of RM codes.

关键词： steganography binary codes message passing matrix embedding steganography binary Reed-Muller codes modified majority-logic decoding algorithm linear block code maximum likelihood decoding algorithm error correcting codes majority-logic algorithm

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Lattice labeling algorithms for vector quantization

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY 1998年第2期8卷 206-220页

作者： Wang, C Cao, HQ Li, WP Tzeng, KK Lehigh Univ Dept Comp Sci & Elect Engn Bethlehem PA 18015 USA

Labeling algorithms for Construction-A and Construction-B lattices with respect to pyramid boundaries are presented, The algorithms are developed based on relations between lattices and linear block codes as well as on transformations among several specifically defined lattices and their translations, The mechanism for the construction of these algorithms can be considered as an extension of that given by Fischer, The algorithms are noted to achieve 100% efficiency in utilizing index bits for binary representations. Furthermore, it is determined that many important lattices (E-8, Lambda(16),...) san be indexed to arbitrary norms and dimensions, The complexity of these algorithms in terms of both memory and computation is quite. low and thus it is possible to develop practical lattice vector quantizers of large norms and high dimensions using these algorithms.

关键词： Construction-A Construction-B decoding encoding labeling lattice lattice vector quantization linear block code vector quantization

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The weight distributions of extended binary primitive BCH codes of length 128

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IEEE TRANSACTIONS ON INFORMATION THEORY 1997年第4期43卷 1364-1371页

作者： Desaki, Y Fujiwara, T Kasami, T NARA INST SCI & TECHNOL GRAD SCH INFORMAT SCIIKOMANARA 63001JAPAN

In our previous work a method was presented to compute the weight distribution of a linear block code by using its trellis diagram. In this correspondence, the method is improved by using the trellis structure of linear block codes. Another method with reduced computational complexity is also proposed which uses the invariant property of a code. With these methods, the weight distributions of all extended binary primitive BCH codes of length 128 are computed, except for those for which the formulas of the weight distribution are known. It turns out that (128, 64, 22) extended binary primitive BCH code is formally self-dual. The probability of an undetectable error for each code is computed and its monotonicity is examined.

关键词： BCH code coset linear block code Reed-Muller code trellis diagram weight distribution

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On the Error Performance Bound of Ordered Statistics Decoding of linear block codes

On the Error Performance Bound of Ordered Statistics Decodin...

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Ad-Hoc and Sensor Networks Symposium

作者： Pawan Dhakal Roberto Garello Shree Krishna Sharma Symeon Chatzinotas Bjorn Ottersten DET - det.polito.it Politecnico di Torino SnT - securityandtrust.lu University of Luxembourg

ISBN: (纸本)9781479966653

In this paper, a novel simplified statistical approach to evaluate the error performance bound of Ordered Statistics Decoding (OSD) of linear block codes (LBC) is investigated. First, we propose a novel statistic which depicts the number of errors contained in the ordered received noisy codeword. Then, simplified expressions for the probability mass function and cumulative distribution function are derived exploiting the implicit statistical independence property of the samples of the received noisy codeword before reordering. Second, we incorporate the properties of this new statistic to derive the simplified error performance bound of the OSD algorithm for all order-I reprocessing. Finally, with the proposed approach, we obtain computationally simpler error performance bounds of the OSD than those proposed in literature for all length LBCs.

关键词： error performance Optical Scanning Device linear block code mass function Bound Ordered DECODING Cumulative distribution function codeword

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CONSTRUCTION OF SOME BINARY linear codeS OF MINIMUM DISTANCE 5

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IEEE TRANSACTIONS ON INFORMATION THEORY 1991年第5期37卷 1429-1432页

作者： CHEN, CL IBM Corporation Poughkeepsie NY USA

A method of constructing binary linear codes is presented that have a minimum Hamming distance of five. Some efficient new codes are obtained. In particular, a (47,36,5) code is obtained that has six more information ... 详细信息

关键词： ERROR-CORRECTING code linear block code

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High Performance, Energy Efficient Chipkill Correct Memory with Multidimensional Parity

IEEE COMPUTER ARCHITECTURE LETTERS

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IEEE COMPUTER ARCHITECTURE LETTERS 2013年第2期12卷 39-42页

作者： Jian, Xun Sartori, John Duwe, Henry Kumar, Rakesh Univ Illiinois Urbana IL USA

It is well-known that a significant fraction of server power is consumed in memory;this is especially the case for servers with chipkill correct memories. We propose a new chipkill correct memory organization that decouples correction of errors due to local faults that affect a single symbol in a word from correction of errors due to device-level faults that affect an entire column, sub-bank, or device. By using a combination of two codes that separately target these two fault modes, the proposed chipkill correct organization reduces code overhead by half as compared to conventional chipkill correct memories for the same rank size. Alternatively, this allows the rank size to be reduced by half while maintaining roughly the same total code overhead. Simulations using PARSEC and SPEC benchmarks show that, compared to a conventional double chipkill correct baseline, the proposed memory organization, by providing double chipkill correct at half the rank size, reduces power by up to 41%, 32% on average over a conventional baseline with the same chipkill correct strength and access granularity that relies on linear block codes alone, at only 1% additional code overhead.

关键词： block codes Error Correction codes Fault Tolerant Computing Granular Computing linear codes Storage Management Server Power Consumption Chipkill Correct Memory Organization Error Correction Device Level Fault Fault Mode code Overhead Reduction Rank Size PARSEC SPEC Granularity Access linear block code DRAM Chips Random Access Memory Low Power Electronics Servers Computer Architecture Chipkill Correct Low Power Reliable Memory DRAM

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Asynchronous secure communication scheme using a new modulation of message on optical chaos

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OPTICAL AND QUANTUM ELECTRONICS 2023年第1期55卷 1-19页

作者： Lin, Lang Li, Qiliang Xi, Xiaohu Hangzhou Dianzi Univ Sch Commun Engn Hangzhou 310018 Zhejiang Peoples R China

An asynchronous secure communication scheme of modulation of message on optical chaos, combining (6, 3) linear block codes (LBC) with majority decoding, is proposed. In this scheme, a semiconductor laser (SL) with electro-optical phase feedback is used to generate an optical chaotic carrier with high complexity. We calculate the sum of the absolute values at adjacent three moments in the chaotic sequence, and divide interval between its maximum and minimum into eight different segments, which are used as the key for generating a new chaotic sequence according to a certain rule. Introducing (6, 3) LBC to encode the message, and using dispersion-compensating fiber (DCF) to eliminate the effect of dispersion induced by single mode fiber (SMF), and then using majority decoding to demodulate the original message at receiving end, we demonstrate that the performance of the bit error rate (BER) in a channel with noise is well improved, and the distortion is greatly reduced. Moreover, our system can realize communication between transmitter and receiver without chaotic synchronization by negotiating these keys through a secret channel.

关键词： Asynchronous Secure communication Optical chaos Semiconductor laser linear block code Majority decoding

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Parity-Check Matrices Separating Erasures From Errors

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IEEE TRANSACTIONS ON INFORMATION THEORY 2013年第6期59卷 3332-3346页

作者： Abdel-Ghaffar, Khaled A. S. Weber, Jos H. Univ Calif Davis Dept Elect & Comp Engn Davis CA 95616 USA Delft Univ Technol NL-2628 CD Delft Netherlands

Most decoding algorithms of linear codes, in general, are designed to correct or detect errors. However, many channels cause erasures in addition to errors. In principle, decoding over such channels can be accomplished by deleting the erased symbols and decoding the resulting vector with respect to a punctured code. For any given linear code and any given maximum number of correctable erasures, parity-check matrices are introduced that yield parity-check equations which do not check any of the erased symbols and which are sufficient to characterize all punctured codes corresponding to this maximum number of erasures. These matrices allow for the separation of erasures from errors to facilitate decoding. Several constructions of such separating parity-check matrices are presented. To reduce decoding complexity, separating parity-check matrices with small number of rows are preferred. The minimum number of rows in a parity-check matrix separating a given maximum number of erasures is called the separating redundancy. Upper and lower bounds on the separating redundancies are derived. In particular, it is shown that the separating redundancies tend to grow linearly with the number of rows in full-rank parity-check matrices of codes. The separating redundancies of some classes of codes are determined for some maximum numbers of erasures.

关键词： Error and erasure decoding linear block code parity-check matrix separating matrix separating redundancy

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