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F-code: An optimized MDS array code

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3rd International Conference on Intelligent Computing

作者： Fan, Jianbo Shou, Lidan Dong, Jinxiang Ningbo Univ Technol Coll Electron & Informat Engn Ningbo 315016 Zhejiang Peoples R China Zhejiang Univ Coll Comp Sci & Technol Hangzhou 310027 Peoples R China

ISBN: (纸本)9783540741701

Based on the research of MDS array code of size nxn in distributed storage system, in this paper, we present a novel encoding scheme called the F-code and prove that the column distance of the F-code is 3, i.e. F-code is a MDS array code given that odd number n is greater than 3 and does not include factor 3. And we also implement a novel decoding algorithm of the F-code. The algorithm only needs two decoding chains in each linear equation group and is able to recover all unknown symbols on two erasure columns. The analysis of F-code shows that our method extends the range of number n in nxn MDS array code and gets lower/reduction algorithmic complexity. Therefore, the reliability of a distributed storage system that features the F-code can be effectively reinforced.

关键词： distributed storage system the F-code encoding scheme MDS property decoding algorithm

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Hardware Complexities of Low-Complexity Chase Reed Solomon Decoders and Comparisons

Hardware Complexities of Low-Complexity Chase Reed Solomon D...

引用

IEEE Asia Pacific Conference on Circuits and Systems (APCCAS)

作者： Wang, Hao Zhang, Wei Wang, Jing Jiang, Zhe Tianjin Univ Sch Elect Informat Engn Tianjin 300072 Peoples R China

ISBN: (纸本)9781457717284;9781457717291

Reed-Solomon (RS) codes are widely used in digital communication and storage systems. Algebraic soft-decision decoding (ASD) of RS codes can achieve significant coding gain over the hard-decision decoding (HDD). Compared with other ASD algorithms, the low-complexity Chase (LCC) decoding algorithm needs less computation complexity with similar or higher coding gain. Several techniques have been applied to reduce the decoding complexity and made the LCC decoding algorithm easier to be implemented by hardware. This paper answers the question that which practical LCC decoder is the most efficient. In addition, decoder complexity comparisons for an example (255, 239) RS code constructed over GF(2(8)) are presented. This paper also provides discussions on how the hardware complexities of LCC decoders change with the decoding parameter and code rate.

关键词： Reed-Solomon codes decoders coding gain Digital communication code rate Computer hardware Cache Memory System Solomon decoding algorithm Reed heart atrium septum defect

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The application of orthogonal designs to wireless communication

The application of orthogonal designs to wireless communicat...

引用

IEEE Information Theory Workshop

作者： Tarokh, V Jafarkhani, H Calderbank, AR AT&T Bell Labs Res Florham Park NJ 07932 USA

ISBN: (纸本)0780344081

We introduce space-block coding, a new paradigm for transmission over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space-block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signal perturbed by noise. decoding is achieved in a simple way using the orthogonal structure of the space-block code and maximum likelihood decoding algorithm is totally based on linear processing at the receiver. Space-black codes are designed to achieve the maximum diversity gain of transmit and receive antennas with the constraint of having a simple decoding algorithm. It is shown that tile classical mathematical framework of orthogonal designs can be applied to construct channel codes which have a simple decoding algorithm, while providing the full spatial diversity order. Space-block codes constructed ill this way only exist for few sporadic values of n and therefore there is a need for a new mathematical theory. In this light, we introduce the theory of Generalized Designs which provides codes for both real and complex constellations for ally number of transmit antennas. Using this theory, we construct space-block codes that achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as PAM. For any arbitrary complex constellation such as PSK and QAM, we construct space-block codes that achieve half of the maximum possible transmission rate for any number of transmit antennas. For the specific cases of two, three and four transmit antennas, we provide space-block codes that achieve respectively the whole, 3/4 and 3/4 of maximum possible transmission rate using arbitrary complex constellations. The best trade-off between tile decoding delay and the number of transmit antennas is also computed and it is shown that the designed code

关键词： transmitting antennas orthogonal designs Codes Block codes CONSTELLATIONS CARRIER SYSTEM Diversity methods maximum likelihood decoding TRANSMISSION RATE encode data Channel coding Receiving antennas decoding algorithm

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New principles in Nuclear Medicine Imaging: A Full Aperture Stereoscopic Imaging Technique

New principles in Nuclear Medicine Imaging: A Full Aperture ...

引用

32nd Annual International Conference of the IEEE Engineering-in-Medicine-and-Biology-Society (EMBC 10)

作者： Strocovsky, Sergio G. Otero, Dino Comis Nacl Energia Atom Ctr Atom Ezeiza Pro Gonzalez & Aragon 15B1802AYA Ezeiza Buenos Aires Argentina Univ Tecnol Nacl Fac Regional Buenos Aires FRBA Buenos Aires DF Argentina

ISBN: (纸本)9781424441242

In nuclear medicine, images of planar scintigraphy and single photon emission computerized tomography (SPECT) obtained through gamma camera (GC) appear to be blurred. Alternatively, coded aperture imaging (CAI) can surpass the quality of GC images, but still it is not extensively used due to the decoding complexity of some images and the difficulty in controlling the noise. Summing up, the images obtained through GC are low quality and it is still difficult to implement CAI technique. Here we present a full aperture imaging (FAI) technique which overcomes the problems of CAI ordinary systems. The gamma radiation transmitted through a large single aperture is edge-encoded, taking advantage of the fact that nuclear radiation is spatially incoherent. The novel technique is tested by means of Monte Carlo method with simple and complex sources. Spatial resolution tests and parallax tests of GC versus FAI were made, and three-dimensional capacities of GC versus FAI were analyzed. Simulations have allowed comparison of both techniques under ideal, identical conditions. The results show that FAI technique has greater sensitivity (similar to 100 times) and greater spatial resolution (> 2.6 times at 40 cm source-detector distance) than that of GC. FAI technique allows to obtain images with typical resolution of GC short source-detector distance but at longer source-detector distance. The FAI decoding algorithm simultaneously reconstructs four different projections, while GC produces only one projection per acquisition. Our results show it is possible to apply an extremely simple encoded imaging technique, and get three-dimensional radioactivity information. Thus GC-based systems could be substituted, given that FAI technique is simple and it produces four images which may feed stereoscopic systems, substituting in some cases, tomographic reconstructions.

关键词： Monte Carlo method Monte Carlo methods SPECT coded aperture imaging decoding algorithm edge encoding full aperture stereoscopic imaging gamma camera image coding image reconstruction image reconstruction image resolution medical image processing nuclear medicine imaging parallax tests planar scintigraphy single photon emission computed tomography single photon emission computerized tomography source-detector distance spatial resolution tests stereo image processing three-dimensional radioactivity information

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One-Level LDPC Lattice Codes for the Relay Channels

One-Level LDPC Lattice Codes for the Relay Channels

引用

Iran Workshop on Communication and Information Theory

作者： Khodaiemehr, Hassan Kiani, Dariush Sadeghi, Mohammad-Reza Amirkabir Univ Technol Fac Math & Comp Sci Tehran Iran

ISBN: (纸本)9781479982356

LDPC lattices were first family of lattices which have efficient decoding algorithm in high dimensions. An LDPC lattice can be constructed from Construction D' and a number of nested LDPC codes. When we consider one code as underlying code of these lattices, one-level LDPC lattices will be obtained. In this paper we propose a new encoding and decoding method for one-level LDPC lattices. We also establish an efficient shaping method for these lattices based on hypercube shaping. Then, based on this encoding and decoding, we propose the implementation of block Markov encoding for one-way relay networks, using obtained one-level LDPC lattice codes. Our proposed decoding algorithm has lower complexity than those given for LDLC lattices.

关键词： crystal lattices low density parity check codes decoding algorithm Relay networks relay decoding Codes relay channel

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A Quantization Schema with Negligible Degradation for LDPC Decoder

A Quantization Schema with Negligible Degradation for LDPC D...

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IEEE International Conference on Wireless Communications, Networking and Information Security (WCNIS)

作者： Wang, Ming-Qiu Xia, Shu-Tao Su, He-Guang Cui, Lai-Zhong Tsinghua Univ Grad Sch Shenzhen Beijing Guangdong Peoples R China

ISBN: (纸本)9781424458516

A quantization schema with negligible degradation for LDPC decoder is proposed. It's based on the decoding algorithm deduced from Belief Propagation algorithm on LLR. The schema offers a quantization criterion for iteration decoder, based on the study of channel outputs. The schema is adaptable for different channel status and quantization scale. Static step lengths for hardware implementation are selected according to the proposed criterion. The performance of the proposed schema is illustrated by both structured and random codes. In simulations for 6-bits quantization, performance loss is negligible. And the schema produces less than 0.01dB degradation for 5-bits quantization above 10(-5) BER and about 0.1dB for 4-bits quantization. There is no error floor of BER even around 10(-7). Simulations show the coverage plays an important role in quantization process. The results of static step lengths are as good as or even better than those of the variable step lengths.

关键词： channel coding decoding algorithm quantization LDPC

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Constant overhead quantum fault-tolerance with quantum expander codes 59

Constant overhead quantum fault-tolerance with quantum expan...

引用

59th IEEE Annual Symposium on Foundations of Computer Science (FOCS)

作者： Fawzi, Omar Grospellier, Antoine Leverrier, Anthony Univ Lyon ENS Lyon UCBL CNRSLIPUMR 5668 F-69007 Lyon France INRIA Paris France

ISBN: (纸本)9781538642306

We prove that quantum expander codes can be combined with quantum fault-tolerance techniques to achieve constant overhead: the ratio between the total number of physical qubits required for a quantum computation with faulty hardware and the number of logical qubits involved in the ideal computation is asymptotically constant, and can even be taken arbitrarily close to 1 in the limit of small physical error rate. This improves on the polylogarithmic overhead promised by the standard threshold theorem. To achieve this, we exploit a framework introduced by Gottesman together with a family of constant rate quantum codes, quantum expander codes. Our main technical contribution is to analyze an efficient decoding algorithm for these codes and prove that it remains robust in the presence of noisy syndrome measurements, a property which is crucial for fault-tolerant circuits. We also establish two additional features of the decoding algorithm that make it attractive for quantum computation: it can be parallelized to run in logarithmic depth, and is single-shot, meaning that it only requires a single round of noisy syndrome measurement.

关键词： decoding algorithm single-shot quantum error correction expander codes percolation

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Embedded Space-Time Block Codes for Concatenated Systems 14

Embedded Space-Time Block Codes for Concatenated Systems

引用

XIV Int Symposium Problems Redundancy Inform Control Syst

作者： Kreshchuk, Alexey Zyablov, Victor Inst Informat Transmiss Problems Moscow Russia

ISBN: (纸本)9781479940509

In this paper we propose new coded modulation for multiple-input and multiple-output (MIMO) communication systems. This coded modulation is a genralised concatenated code. Its inner code is embedded Golden code which we introduce in this paper with a decoding algorithm. Its outer code is a product code with component Reed-Solomon code. We use iterative decoding algorithm for this product code. The performance of the proposed system is estimated with a computer simulation.

关键词： Gold codes MIMO communication Reed-Solomon codes concatenated codes iterative decoding modulation coding product codes space-time block codes MIMO communication systems RS code coded modulation component Reed-Solomon code computer simulation embedded Golden code embedded space-time block codes generalised concatenated code iterative decoding algorithm multiple-input and multiple-output communication systems product code Concatenated codes decoding Iterative decoding MIMO Modulation Space-time codes Vectors Product codes modulation coding Reed-Solomon codes Concatenated codes Iterative decoding MIMO communication Gold codes space-time codes decoding algorithm Computer Simulation multiple input multiple output systems decoding space time block coding Block codes COMMUNICATION SYSTEMS

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Low-complexity decoders for non-binary turbo codes 10

Low-complexity decoders for non-binary turbo codes

引用

10th IEEE International Symposium on Turbo Codes & Iterative Information Processing (ISTC)

作者： Klaimi, Rami Nour, Charbel Abdel Douillard, Catherine Farah, Joumana CNRS UMR 6285 Lab STICC IMT Atlantique Brest France Lebanese Univ Fac Engn Roumieh Lebanon

ISBN: (纸本)9781538670484

Following the increasing interest in non-binary coding schemes, turbo codes over different Galois fields have started to be considered recently. While showing improved performance when compared to their binary counterparts, the decoding complexity of this family of codes remains a main obstacle to their adoption in practical applications. In this work, a new low-complexity variant of the Min-Log-MAP algorithm is proposed. Thanks to the introduction of a bubble sorter for the different metrics used in the Min-Log-MAP decoder, the number of required computations is significantly reduced. A reduction by a factor of 6 in the number of additions and compare-select operations can be achieved with only a minor impact on error rate performance. With the use of an appropriate quantization, the resulting decoder paves the way for a future hardware implementation.

关键词： Non-binary turbo codes decoding algorithm bubble check complexity reduction

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An adaptable binary entropy coder

An adaptable binary entropy coder

引用

Data Compression Conference (DCC 2001)

作者： Kiely, A Klimesh, M CALTECH Jet Prop Lab Pasadena CA 91109 USA

ISBN: (纸本)0769510310

We present a novel entropy coding technique which is based on recursive interleaving of variable-to-variable length binary source codes. The encoding is adaptable in that each bit to be encoded may have an associated probability estimate which depends on previously encoded bits. The technique may have advantages over arithmetic coding. The technique can achieve arbitrarily small redundancy, and admits a simple and fast decoder. We discuss code design and performance estimation methods, as well as practical encoding and decoding algorithms.

关键词： Binary entropy coding ENCODER Statistical analysis decoding algorithm Source code Entropy coding arithmetic coding Performance Evaluation

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