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A MacWilliams formula for convolutional codes

INTERNATIONAL JOURNAL OF NUMBER THEORY 2007年第2期3卷 191-206页

作者： Sole, Patrick Zinoviev, Dmitrii CNRS I3S F-06903 Sophia Antipolis France Inst Problems Informat Moscow 127994 Russia

Regarding convolutional codes as polynomial analogues of arithmetic lattices, we derive a Poisson-Jacobi formula for their trivariate weight enumerator. The proof is based on harmonic analysis on locally compact abeli... 详细信息

关键词： local field convolutional code Poisson formula Krawtchouk polynomial

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State Spaces of convolutional codes

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Designs, codes, and Cryptography 1997年第3期10卷 361-369页

作者： Wan, Zhe-Xian Institute of Systems Science Chinese Academy of Sciences Beijing China Department of Information Theory Lund University Lund Sweden

There are various definitions of convolutional codes and each definition leads to a definition of code state space. In the usual definition of a convolutional code generated by a rational encoding matrix input sequences can be any Laurent series. It is proved that restricting input sequences to be rational functions or restricting output sequences to be finite do not change the code state space, and that restricting both input and output sequences to be finite may change the code state space.

关键词： convolutional code Group code State space

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RCPC codeS PERFORMANCE ANALYSIS USING NON-PUNCTURED EQUIVALENT convolutional codeS

RCPC CODES PERFORMANCE ANALYSIS USING NON-PUNCTURED EQUIVALE...

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IEEE International Conference on Communication, Networks and Satellite (COMNETSAT)

作者： Sari, Lydia Atma Jaya Catholic Univ Indonesia Dept Elect Engn Jakarta Indonesia

ISBN: (纸本)9781479951918

Rate Compatible Punctured convolutional (RCPC) code is a sub-class of convolutional code which allows varied levels of data protection to suit different types of data. RCPC is becoming extensively used in telecommunication systems as it offers bandwidth efficiency and simpler hardware implementation compared to convolutional coding, with comparable performance. RCPC codes are attained by puncturing several of the redundancy bits of convolutional codes. As accurate analysis of the bit error probability for a punctured convolutional encoder using state diagram and transfer function is not a straightforward process, in this paper we use non-punctured equivalent convolutional code to represent the punctured code. There are numerous puncturing patterns to yield RCPC codes from certain convolutional mother code. Our simulation results in AWGN and Rayleigh fading channels show that the same code rates yielded by different puncturing patterns will result in different code performance. Therefore, puncturing pattern is one of the key considerations in generating an RCPC code as it markedly affects the code performance.

关键词： RCPC convolutional code puncturing pattern non-punctured equivalent code

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Performance of a Maximum-Likelihood Decoding Metric for convolutional coded FH/BFSK Systems over AWGN Channels under Partial-Band Jamming

Performance of a Maximum-Likelihood Decoding Metric for Conv...

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15th IEEE International Conference on Communication Technology (ICCT)

作者： Quan, Houde Zhao, Huan Cui, Peizhang Mech Engn Coll Shijiazhuang 050003 Peoples R China

ISBN: (纸本)9781479900749

To provide an upper bound on the performance of the existing decoding metrics for convolutional coded frequency-hopped binary frequency-shift-keying (FH/BFSK) spread-spectrum communication system, an optimum maximum-likelihood (ML) metric is derived operating over additive white Gaussian noise (AWGN) channels under partial-band jamming (PBJ). It is shown that the proposed ML metric requires the side information of the signal energy, the noise-plus-jamming power spectral density and the computation of logarithm Marcum-Q function to implement. Moreover, a simplified suboptimum ML metric is derived, and its union bound on bit error rate (BER) serves as a tight upper bound on BER for the optimum ML metric. A lower BER bound is also obtained for the ML metric. Tightness of these bounds is validated by simulations. Performance comparison under the worst-case PBJ shows that the proposed ML metric outperforms various existing metrics over AWGN channels.

关键词： FH/BFSK convolutional code maximum-likelihood decoding metric union bound

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THE VLSI DESIGN OF AN ERROR-TRELLIS SYNDROME DEcodeR FOR CERTAIN convolutional-codeS

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IEEE TRANSACTIONS ON COMPUTERS 1986年第9期35卷 781-789页

作者： REED, IS TRUONG, TK JENSEN, JM HSU, IS CALTECH JET PROP LABPASADENACA 91109

In this paper a recursive algorithm using the error-trellis decoding technique is developed to decode certain convolutional codes (CC"s). An example, illustrating the VLSI architecture of such a decoder, is given for a dual-k CC. It is demonstrated that such a decoder can be realized readily on a single chip with NMOS technology.

关键词： convolutional code VLSI Wyner-Ash code error-trellis syndrome decoder

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Generalized punctured convolutional codes

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IEEE COMMUNICATIONS LETTERS 2005年第12期9卷 1070-1072页

作者： Uchôa, BF Souza, RD Pimentel, C Lin, MC Univ Fed Santa Catarina EEL BR-88040900 Florianopolis SC Brazil CPGEI CEFET BR-80230901 Curitiba Parana Brazil UFPE CODEC DES Recife PE Brazil Natl Taiwan Univ Dept Elect Engn Taipei 10764 Taiwan

This letter introduces the class of generalized punctured convolutional codes (GPCCs), which is broader than and encompasses the class of the standard punctured convolutional codes (PCCs). A code in this class can be represented by a trellis module, the GPCC trellis module, whose topology resembles that of the minimal trellis module. The GPCC trellis module for a PCC is isomorphic to the minimal trellis module. A list containing GPCCs with better distance spectrum than the best known PCCs with same code rate and trellis complexity is presented.

关键词： .distance spectrum trellis complexity Generalized Punctured convolutional GPCCs trellis module minimal trellis convolutional code

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Comparative Analysis of convolutional codes based on ML Decoding 2

Comparative Analysis of Convolutional Codes based on ML Deco...

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2nd International Conference on Communication Control and Intelligent Systems (CCIS)

作者： Agrawal, Tarun Kumar, Anjan Saraswat, Shelesh Krishna GLA Univ Dept Elect & Commun Mathura India

ISBN: (纸本)9781509032105

Viterbi algorithm is based on Maximum Likelihood Decoding Method. It finds a path from 2(k) total path through trellis that maximizes the path conditional probability. During decoding it compares the metric of all partial path entering each state. this paper involves brief information about convolutional code in terms of strategies of encoding and decoding of convolutional codes and also, Recursive Systematic convolutional Encoder is designed with BPSK Modulation and decoding is done by use of ML Decoding Method, compares the BER vs SNR performance at different code rates and find that as SNR increases the BER improves and also as number of bits are increases the performance of communication system also improves. At 3 db SNR the BER is 10 boolean AND-2, when the number of bits are 2048 and 4096 at 4db SNR the BER is close to 10 boolean AND-3.

关键词： convolutional code LTE ML Decoding MAP Decoding Burst Error HSDPA Interleaver

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On the union bound applied to convolutional codes

On the union bound applied to convolutional codes

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54th IEEE Vehicular Technology Conference (VTC 2001)

作者： Lassing, J Ottosson, T Ström, E Chalmers Univ Technol Dept Signals & Syst S-41296 Gothenburg Sweden

ISBN: (纸本)0780370058

To evaluate the performance of a convolutional code it is common to use a union bound on either the bit-error rate or the first-event error rate. Since these bounds are given as infinite sums they must be truncated to be evaluated. However, as the tail of the infinite sum is discarded. the upper bound turns into an approximation. In this paper, two methods to evaluate the union bound while taking the summation tail into account and thus maintaining the upper bound are described. The first method is based on a state matrix description of the convolutional encoder, while the second method is based on the transfer function. Results are given that compare the upper bounds and the truncated bound (approximation) to computer simulations. The standard rule-of-thumb that the union bound is tight as long as the error rates are below 10(-3) is readily seen to be valid.

关键词： convolutional code union bound truncation of union bound state transition matrix transfer function bound

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Robust Decoding of Concatenated RS-convolutional codes over the Quasi-Static Fading Channel with No Explicit CSI Acquisition 82

Robust Decoding of Concatenated RS-Convolutional Codes over ...

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IEEE 82nd Vehicular Technology Conference (VTC Fall)

作者： Yuan, Haifeng Kam, Pooi Yuen Natl Univ Singapore Dept Elect & Comp Engn Singapore 117576 Singapore

ISBN: (纸本)9781479980918

Accurate channel state information (CSI) is crucial for reliable decoding over fading channels. In many existing works, the CSI acquisition relies greatly on accurate knowledge of the channel model information (CMI), which includes, in particular, the power spectrum of the fading process and the statistical distribution of the fading gain. In practice, it may be difficult to obtain or keep track of the CMI accurately. In this paper, we consider the decoding of Reed-Solomon convolutional concatenated (RSCC) codes over the quasi-static fading channel, and propose a robust, decision-directed, soft-output convolutional decoder which does not require explicit CSI acquisition. Simulation result shows that the proposed decoder has a lower bit-error rate for convolutional decoding than the conventional soft-output Viterbi algorithm and the BCJR algorithm with pilot-symbol-assisted channel estimation. The advantage of the former in terms of the accuracy of soft-decision output is demonstrated by the superiority of word-error performance in the RSCC decoding.

关键词： robust receiver design quasi-static fading channel SOVA convolutional code Reed-Solomon code

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Search for High-Rate Punctured convolutional codes through Transformed Identical codes

Search for High-Rate Punctured Convolutional Codes through T...

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39th Symposium on Information Theory and Its Applications (SITA)

作者： Moriya, Sen Kikuchi, Kana Sasano, Hiroshi Kindai Univ Sch Sci & Engn Higashiosaka Osaka 5778502 Japan

In this study, we consider techniques to search for high-rate punctured convolutional code (PCC) encoders by rearranging row vectors of identical-encoder generator matrices. One well-known method to obtain a good PCC encoder is to perform an exhaustive search of all candidates. However, this approach is time-intensive. An exhaustive search with a rate R-G = 1/2 original encoder requires a relatively short time, whereas that with an R-G = 1/3 or lower original encoder takes significantly longer. The encoders with lower-rate original encoders are expected to create better PCC encoders. Thus, this paper proposes a method that uses exhaustive search results with rate R-G = 1/2 original encoders, and rearranges row vectors of identical-encoder generator matrices to create PCCs with a lower rate original code. Further, we provide PCC encoders obtained by searches that utilize our method.

关键词： convolutional code punctured code identical code weight spectrum

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