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On a decoding algorithm by superposition for binary cyclic codes for certain burst errors

ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE 1996年第4期79卷 74-81页

作者： Ogino, A Kohnosu, T Hirasawa, S Nishijima, T WASEDA UNIV SCH SCI & ENGNTOKYO 169JAPAN HOSEI UNIV COLL ENGNKOGANEITOKYO 184JAPAN

Cyclic codes are often used for the purpose of correcting burst errors in digital transmission and recording systems. Since the implementations of the encoding and syndrome calculations of these codes are simple, these codes have superior properties from a practical perspective. In this paper, an effective decoding method is given for certain burst errors (multiple solid-burst errors) that are contained within the detected errors resulting from a binary cyclic ''predecoding'' process, where the precoding process for burst error correction is terminated at the detection stage. Such burst errors can be expressed as random errors by superimposing a copy of itself that has been cyclically shifted by one bit. So, by performing random error decoding on a version of the received sequence that has been superimposed with a one-bit cyclically shifted copy of itself, burst errors can be accurately corrected. This decoding method completely preserves the correction capacity of the precede and is applicable to any binary cyclic code with a minimum distance of at least 5. The correctable multiple solid-burst errors depend on the minimum distance of the code. Furthermore, by applying this technique to interleaved random error-correction codes for the purpose of correcting burst errors, it is shown that it is possible to extend the length of correctable burst errors.

关键词： cyclic codes decoding algorithm superposition method for decoding burst errors

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The application of orthogonal designs to wireless communication

The application of orthogonal designs to wireless communicat...

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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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Graphical codes revisited

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IEEE TRANSACTIONS ON INFORMATION THEORY 1997年第1期43卷 136-146页

作者： Jungnickel, D Vanstone, SA UNIV WATERLOO DEPT COMBINATOR & OPTIMIZAT WATERLOO ON N2L 3G1 CANADA

It is well-known that the set of all even subgraphs of a connected graph G on p vertices with q edges forms a binary linear code C = C-E(G) with parameters [q, q - p + 1, g], where g is the girth of G. Such codes were studied systematically by Bredeson and Hakimi [7], [14] who were concerned with the problems of augmenting C to a larger [q, k, g]-code and of efficiently decoding such augmented graphical codes, We will give a new approach to these problems by requiring the augmented codes to be graphical (i,e,, they should still consist of spanning subgraphs of G), On one hand, we present two construction methods which turn out to contain the methods proposed by Hakimi and Bredeson [14] as special cases (even though it is not clear from their paper that their augmented codes are in fact graphical), As we will show, this not only gives a better understanding of their construction, it also results in augmenting codes of larger dimension. We look at the case of 1-error-correcting graphical codes in some detail, In particular, we show how to obtain the extended Hamming codes as ''purely'' graphical codes by our approach, On the other hand, we follow a suggestion of Ntafos and Hakimi [26] and use techniques from combinatorial optimization to give decoding procedures for graphical codes which turn out to be considerably more efficient than the approach via majority logic decoding proposed by Bredeson and Hakimi. We also consider the decoding problem for the even graphical code based on the complete graph K-2n in more detail: we discuss an efficient hardware implementation of an encoding/decoding scheme for these codes and we also show that things may be arranged in such a way that one can also correct all adjacent double errors, Finally, we briefly discuss nonlinear graphical codes.

关键词： graphical code binary code decoding algorithm Chinese postman problem

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A new algorithm for RNS decoding

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS 1996年第12期43卷 998-1001页

作者： Wang, Y AbdElBarr, M KING FAHD UNIV PETR & MINERALS COLL COMP SCI & ENGNDEPT COMMUN ENGNDHAHRAN 31261SAUDI ARABIA

In this brief, a divide-and-conquer based RNS (residue number system) decoding algorithm is proposed. The basic idea of this algorithm is to decompose a set of moduli into groups each of size two moduli and to decode a given number in a two moduli representation. The time complexity of the algorithm used is O(log n), where n is the size of the moduli set. There is no assumption made on the elements of the module set. In addition, the algorithm requires less ROM size and smaller size module adders compared to those requried by existing approaches.

关键词： adders computational complexity decoding divide and conquer methods residue number systems RNS decoding ROM size decoding algorithm divide-and-conquer based RNS module adders module set time complexity two moduli representation divide and conquer methods adders residue number systems decoding algorithm algorithms complexity classes decoding

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A new, fast, and efficient image codec based on set partitioning in hierarchical trees

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY 1996年第3期6卷 243-250页

作者： Said, A Pearlman, WA RENSSELAER POLYTECH INST DEPT ELECT COMP & SYST ENGNTROYNY 12180

Embedded zerotree wavelet (EZW) coding, introduced by J. M. Shapiro, is a very effective and computationally simple technique for image compression, Here we offer an alternative explanation of the principles of its operation, so that the reasons for its excellent performance can be better understood, These principles are partial ordering by magnitude with a set partitioning sorting algorithm, ordered bit plane transmission, and exploitation of self-similarity across different scales of an image wavelet transform, Moreover, we present a new and different implementation based on set partitioning in hierarchical trees (SPIHT), which provides even better performance than our previously reported extension of EZW that surpassed the performance of the original EZW, The image coding results, calculated from actual file sizes and images reconstructed by the decoding algorithm, are either comparable to or surpass previous results obtained through much more sophisticated and computationally complex methods, In addition, the new coding and decoding procedures are extremely fast, and they can be made even faster, with only small loss in performance, by omitting entropy coding of the bit stream by arithmetic code.

关键词： set partitioning Partial ordering Image compression decoding algorithm Data compression Entropy coding Hierarchical arithmetic coding codecs bit stream

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FAST SEQUENTIAL-decoding algorithm-BASED ON DYNAMIC SEARCHING STRATEGY

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IEE PROCEEDINGS-COMMUNICATIONS 1994年第5期141卷 312-316页

作者： LEE, CY YANG, WW JENG, LF Dept. of Electron. Eng. Nat. Chiao Tung Univ. Hsinchu Taiwan

The authors present a new sequential decoding algorithm based on dynamic searching strategy to improve decoding efficiency. The searching strategy is to exploit both 'sorting' and 'path recording' techniques. By means of sorting, it is possible to identify the correct path in a very fast way and then, by the recording, the bit sequence can be recovered without degrading decoding performance. The authors also develop a conditional resetting scheme to overcome the buffer overflow problem encountered in conventional sequential decoding algorithms. Simulation results show that, for a given code, the decoding efficiency remains the same as that obtained from maximum likelihood function by appropriately selecting sorting length and decoding depth. In addition, this algorithm can easily be mapped onto an area-efficient VLSI architecture to implement long constraint length convolutional decoders for high-speed digital communications.

关键词： decoding algorithm decoding EFFICIENCY DYNAMIC SEARCHING STRATEGY

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Implementation of coding and encryption in satellite channel

Implementation of coding and encryption in satellite channel

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1996 International Conference on Communication Technology

作者： Xie, YX Chen, J Fu, CG COMMUN ENGN INST DEPT RADIO COMMUNNANJING 210016PEOPLES R CHINA

ISBN: (纸本)7505336355

An implementation of coding and encryption for data in a low Earth orbit satellite channel is presented. A system of block coding and block cipher is designed to improve the noise performance and for data security, respectively. The Reed-Muller code is adopted as the coding scheme and an improved algorithm based on the Reed algorithm is used as decoding algorithm. A supercipher system combined with a block cipher and a stream cipher is put forward to compensate the shortage of total encryption keys brought about by the short block length of the block cipher. For a system with a bit rate as high as 10/sup 6/ b/s, an EPROM array is used and one search process could implement both the coding and encryption.

关键词： satellite communication cryptography encoding decoding block codes Reed-Muller codes EPROM channel coding telecommunication channels noise performance data encryption data coding data security low Earth orbit satellite channel Reed-Muller code decoding algorithm Reed algorithm supercipher system block cipher stream cipher encryption keys block length bit rate EPROM array search proces

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A decoding algorithm AND SOME PROPERTIES OF BOINCK AND TILBORG T-EC/AUED CODE

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1993年第9期E76A卷 1535-1536页

作者： YOSHIDA, K JINUSHI, H SAKANIWA, K NTT Data Communications Systems Corp Tokyo Japan

We propose a decoding algorithm for the t-EC/AUED code proposed by Boinck and Tilborg. The proposed algorithm also reveals some remarkable properties of the code.

关键词： T-EC/AUED CODES SYMMETRICAL ERROR UNIDIRECTIONAL ERROR BURST-ERROR decoding algorithm

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GENERALIZED KEY-EQUATION OF REMAINDER decoding algorithm FOR REED SOLOMON CODES

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IEEE TRANSACTIONS ON INFORMATION THEORY 1992年第6期38卷 1801-1807页

作者： MORII, M KASAHARA, M KYOTO INST TECHNOL DEPT ELECTR & INFORMAT SCIKYOTO 606JAPAN

A new key-equation of the remainder decoding algorithm is presented. It is noted that the key-equation presents a general relationship between the errors on the received codeword and the coefficients of the remainder polynomial. It is shown that we can derive several key-equations proposed by Welch-Berlekamp and others from our new key-equation. Furthermore useful properties of the key-equations in fast decoding of Reed-Solomon codes are given.

关键词： CODING THEORY decoding algorithm REED SOLOMON CODES REMAINDER decoding WELCH BERLEKAMP algorithm

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MODIFIED TIME-DOMAIN algorithm FOR decoding REED-SOLOMON CODES

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IEEE TRANSACTIONS ON COMMUNICATIONS 1993年第7期41卷 1036-1038页

作者： SHAYAN, YR LENGOC, T CONCORDIA UNIV DEPT ELECT & COMP ENGNMONTREAL H3G 1M8QUEBECCANADA

A technique to reduce the number of inversions in the time-domain decoding algorithm based on an algebraic decoder (Blahut's decoder) is introduced. It is proved that the modified algorithm is equivalent to the or... 详细信息

关键词： Reed-Solomon codes decoders Inversion decoding algorithm algorithms decoding Modified Equivalent

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