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Soft Decoding Scheme of Convolution Code Combined with Huffman Coding
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作者 郭东亮 陈小蔷 吴乐南 《Journal of Southeast University(English Edition)》 EI CAS 2002年第3期208-211,共4页
This paper proposes a modification of the soft output Viterbi decoding algorithm (SOVA) which combines convolution code with Huffman coding. The idea is to extract the bit probability information from the Huffman codi... This paper proposes a modification of the soft output Viterbi decoding algorithm (SOVA) which combines convolution code with Huffman coding. The idea is to extract the bit probability information from the Huffman coding and use it to compute the a priori source information which can be used when the channel environment is bad. The suggested scheme does not require changes on the transmitter side. Compared with separate decoding systems, the gain in signal to noise ratio is about 0 5-1.0 dB with a limi... 展开更多
关键词 soft output Viterbi decoding a priori information Huffman coding convolution code
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Improved Design and SOVA Algorithm for Serial Concatenated Convolutional Code 被引量:2
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作者 万蕾 匡镜明 《Journal of Beijing Institute of Technology》 EI CAS 2001年第2期180-185,共6页
To improve the performance of the short interleaved serial concatenated convolutional code(SCCC) with low decoding iterative times, the structure of Log MAP algorithm is introduced into the conventional SOVA decoder... To improve the performance of the short interleaved serial concatenated convolutional code(SCCC) with low decoding iterative times, the structure of Log MAP algorithm is introduced into the conventional SOVA decoder to improve its performance at short interleaving delay. The combination of Log MAP and SOVA avoids updating the matrices of the maximum path, and also makes a contribution to the requirement of short delay. The simulation results of several SCCCs show that the improved decoder can obtain satisfied performance with short frame interleaver and it is suitable to the high bit rate low delay communication systems. 展开更多
关键词 serial concatenated convolutional code Turbo code iterative decoder WCDMA
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Blind recognition of k/n rate convolutional encoders from noisy observation 被引量:14
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作者 Li Huang Wengu Chen +1 位作者 Enhong Chen Hong Chen 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2017年第2期235-243,共9页
Blind recognition of convolutional codes is not only essential for cognitive radio, but also for non-cooperative context. This paper is dedicated to the blind identification of rate k/n convolutional encoders in a noi... Blind recognition of convolutional codes is not only essential for cognitive radio, but also for non-cooperative context. This paper is dedicated to the blind identification of rate k/n convolutional encoders in a noisy context based on Walsh-Hadamard transformation and block matrix (WHT-BM). The proposed algorithm constructs a system of noisy linear equations and utilizes all its coefficients to recover parity check matrix. It is able to make use of fault-tolerant feature of WHT, thus providing more accurate results and achieving better error performance in high raw bit error rate (BER) regions. Moreover, it is more computationally efficient with the use of the block matrix (BM) method. © 2017 Beijing Institute of Aerospace Information. 展开更多
关键词 Cognitive radio convolution convolutional codes Error correction Hadamard matrices Hadamard transforms Linear transformations Mathematical transformations Matrix algebra Signal encoding
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Blind reconstruction of convolutional code based on segmented Walsh-Hadamard transform 被引量:12
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作者 Fenghua Wang Hui Xie Zhitao Huang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2014年第5期748-754,共7页
Walsh-Hadamard transform (WriT) can solve linear error equations on Field F2, and the method can be used to recover the parameters of convolutional code. However, solving the equations with many unknowns needs enorm... Walsh-Hadamard transform (WriT) can solve linear error equations on Field F2, and the method can be used to recover the parameters of convolutional code. However, solving the equations with many unknowns needs enormous computer memory which limits the application of WriT. In order to solve this problem, a method based on segmented WriT is proposed in this paper. The coefficient vector of high dimension is reshaped and two vectors of lower dimension are obtained. Then the WriT is operated and the requirement for computer memory is much reduced. The code rate and the constraint length of convolutional code are detected from the Walsh spectrum. And the check vector is recovered from the peak position. The validity of the method is verified by the simulation result, and the performance is proved to be optimal. 展开更多
关键词 convolutional code blind reconstruction Walsh-Hadamard transform (WriT) tinear error equation.
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Construction of Regular Rate-Compatible LDPC Convolutional Codes 被引量:2
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作者 Liwei Mu Chulong Liang +1 位作者 Zhiyong Liu Daru Pan 《China Communications》 SCIE CSCD 2016年第8期97-102,共6页
In this paper, we propose a new method to derive a family of regular rate-compatible low-density parity-check(RC-LDPC) convolutional codes from RC-LDPC block codes. In the RC-LDPC convolutional family, each extended... In this paper, we propose a new method to derive a family of regular rate-compatible low-density parity-check(RC-LDPC) convolutional codes from RC-LDPC block codes. In the RC-LDPC convolutional family, each extended sub-matrix of each extended code is obtained by choosing specified elements from two fixed matrices HE1K and HE1K, which are derived by modifying the extended matrices HE1 and HE2 of a systematic RC-LDPC block code. The proposed method which is based on graph extension simplifies the design, and prevent the defects caused by the puncturing method. It can be used to generate both regular and irregular RC-LDPC convolutional codes. All resulted codes in the family are systematic which simplify the encoder structure and have maximum encoding memories which ensure the property. Simulation results show the family collectively offer a steady improvement in performance with code compatibility over binary-input additive white Gaussian noise channel(BI-AWGNC). 展开更多
关键词 binary-input additive white Gaussian noise channel(BI-AWGNC) extended matrices rate-compatible low-density parity-check(RC-LDPC) convolutional codes
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Construction of Rate-Compatible(RC) Low-Density Parity-Check(LDPC) Convolutional Codes Based on RC-LDPC Block Codes 被引量:1
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作者 穆丽伟 韩国军 刘志勇 《Journal of Shanghai Jiaotong university(Science)》 EI 2016年第6期679-683,共5页
In this paper,a family of rate-compatible(RC) low-density parity-check(LDPC) convolutional codes can be obtained from RC-LDPC block codes by graph extension method.The resulted RC-LDPC convolutional codes,which are de... In this paper,a family of rate-compatible(RC) low-density parity-check(LDPC) convolutional codes can be obtained from RC-LDPC block codes by graph extension method.The resulted RC-LDPC convolutional codes,which are derived by permuting the matrices of the corresponding RC-LDPC block codes,are systematic and have maximum encoding memory.Simulation results show that the proposed RC-LDPC convolutional codes with belief propagation(BP) decoding collectively offer a steady improvement on performance compared with the block counterparts over the binary-input additive white Gaussian noise channels(BI-AWGNCs). 展开更多
关键词 rate-compatible(RC) low-density parity-check(LDPC) convolutional codes systematic maximum encoding memory belief propagation(BP) decoding
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Ensemble of High Performance Structured Binary Convolutional LDPC Codes with Moderate Rates 被引量:1
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作者 Liwei Mu 《China Communications》 SCIE CSCD 2020年第10期195-205,共11页
An algebraic construction methodology is proposed to design binary time-invariant convolutional low-density parity-check(LDPC)codes.Assisted by a proposed partial search algorithm,the polynomialform parity-check matri... An algebraic construction methodology is proposed to design binary time-invariant convolutional low-density parity-check(LDPC)codes.Assisted by a proposed partial search algorithm,the polynomialform parity-check matrix of the time-invariant convolutional LDPC code is derived by combining some special codewords of an(n,2,n−1)code.The achieved convolutional LDPC codes possess the characteristics of comparatively large girth and given syndrome former memory.The objective of our design is to enable the time-invariant convolutional LDPC codes the advantages of excellent error performance and fast encoding.In particular,the error performance of the proposed convolutional LDPC code with small constraint length is superior to most existing convolutional LDPC codes. 展开更多
关键词 algebraic construction (n 2 n−1)codes convolutional low-density parity-check(LDPC)codes fast encoding maximum achievable syndrome former memory large girth
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New Parallel Interference Cancellation for Convolutionally Coded CDMA Systems
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作者 Xu Guo-xiong Gan Liang-cai Huang Tian-xi 《Wuhan University Journal of Natural Sciences》 CAS 2004年第1期78-82,共5页
Based on BCJR algorithm proposed by Bahlet al and linear soft decision feedback,a reduced-complexity parallel interference cancellation(simplified PIC)for convolutionally coded DS CDMA systems is proposed.By computer ... Based on BCJR algorithm proposed by Bahlet al and linear soft decision feedback,a reduced-complexity parallel interference cancellation(simplified PIC)for convolutionally coded DS CDMA systems is proposed.By computer simulation,we compare the simplified PIC with the exact PIC.It shows that the simplified PIC can achieve the performance close to the exact PIC if the mean values of coded symbols are linearly computed in terms of the sum of initiala prior log-likelihood rate(LLR)and updateda prior LLR,while a significant performance loss will occur if the mean values of coded symbols are linearly computed in terms of the updateda prior LLR only.Meanwhile,we also compare the simplified PIC with MF receiver and conventional PICs.The simulation results show that the simplified PIC dominantly outperforms the MF receiver and conventional PICs,at signal-noise rate(SNR)of 7 dB,for example,the bit error rate is about 10^(-4)for the simplified PIC,which is far below that of matched-filter receiver and conventional PIC. 展开更多
关键词 convolutionally coded CDMA parallel interference cancellation BCJR
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Performance of Convolutionally Coded Multicarrier DS-CDMA System
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作者 SONG Li-xin HUANG Tian-shu DU Guang-yu 《Semiconductor Photonics and Technology》 CAS 2005年第4期281-286,共6页
A new convolutionally coded direct sequence (DS) CDMA system is proposed. The outputs of a convolutional encoder modulate multiple band-limited DS-CDMA waveforms. The receiver detects and combines signals for the desi... A new convolutionally coded direct sequence (DS) CDMA system is proposed. The outputs of a convolutional encoder modulate multiple band-limited DS-CDMA waveforms. The receiver detects and combines signals for the desired user and feeds a soft-decision Viterbi decoder. The performance of this system is compared to that of a convolutionally coded single carrier DS CDMA system with a Rake receiver. At roughly equivalent receiver complexity, results will demonstrate superior performance of the coded multicarrier system. 展开更多
关键词 convolutional code Rayleigh fading Multicarrier CDMA Frequency diversity Narrow-band interference
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NEW METHOD TO RECOVER INTERNET PACKET LOSSES USING(2,1,m)SYSTEMATIC CONVOLUTIONAL CODES
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作者 Peng Bo Wei Gang(Institute of Electron. Eng. and Control, South China University of Technology,Guangzhou 510640) 《Journal of Electronics(China)》 2002年第2期199-203,共5页
A new method to recover packet losses using (2,1,m) convolutional codes is proposed. The erasure correcting decoding algorithm and the decoding determinant theorem is presented. It is also proved that the codes with o... A new method to recover packet losses using (2,1,m) convolutional codes is proposed. The erasure correcting decoding algorithm and the decoding determinant theorem is presented. It is also proved that the codes with optimal distance profile have also optimal delay characteristic. Simulation results show that the proposed method can recover the packet losses more elliciently than RS codes over different decoding delay conditions and thus suits for different packet network delav conditions. 展开更多
关键词 convolutional code: Packet loss Erasure correcting codes
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Joint Source-Channel Decoding of EVRC Speech Encoder Using Residual Redundancy
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作者 阿哈麦德 尤肖虎 高西奇 《Journal of Southeast University(English Edition)》 EI CAS 2002年第2期103-107,共5页
The enhanced variable rate codec (EVRC) is a standard for the 'Speech ServiceOption 3 for Wideband Spread Spectrum Digital System,' which has been employed in both IS-95cellular systems and ANSI J-STC-008 PCS ... The enhanced variable rate codec (EVRC) is a standard for the 'Speech ServiceOption 3 for Wideband Spread Spectrum Digital System,' which has been employed in both IS-95cellular systems and ANSI J-STC-008 PCS (personal communications systems). This paper concentrateson channel decoders that exploit the residual redundancy inherent in the enhanced variable ratecodec bitstream. This residual redundancy is quantified by modeling the parameters as first orderMarkov chains and computing the entropy rate based on the relative frequencies of transitions.Moreover, this residual redundancy can be exploited by an appropriately 'tuned' channel decoder toprovide substantial coding gain when compared with the decoders that do not exploit it. Channelcoding schemes include convolutional codes, and iteratively decoded parallel concatenatedconvolutional 'turbo' codes. 展开更多
关键词 residual redundancy convolutional codes turbo codes
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A novel construction method of QC-LDPC codes based on the subgroup of the finite field multiplicative group for optical transmission systems 被引量:3
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作者 袁建国 周光香 +3 位作者 高文春 王永 林金朝 庞宇 《Optoelectronics Letters》 EI 2016年第1期61-64,共4页
According to the requirements of the increasing development for optical transmission systems,a novel construction method of quasi-cyclic low-density parity-check(QC-LDPC) codes based on the subgroup of the finite fiel... According to the requirements of the increasing development for optical transmission systems,a novel construction method of quasi-cyclic low-density parity-check(QC-LDPC) codes based on the subgroup of the finite field multiplicative group is proposed.Furthermore,this construction method can effectively avoid the girth-4 phenomena and has the advantages such as simpler construction,easier implementation,lower encoding/decoding complexity,better girth properties and more flexible adjustment for the code length and code rate.The simulation results show that the error correction performance of the QC-LDPC(3 780,3 540) code with the code rate of 93.7% constructed by this proposed method is excellent,its net coding gain is respectively 0.3dB,0.55dB,1.4dB and 1.98dB higher than those of the QC-LDPC(5 334,4 962) code constructed by the method based on the inverse element characteristics in the finite field multiplicative group,the SCG-LDPC(3 969,3 720) code constructed by the systematically constructed Gallager(SCG) random construction method,the LDPC(32 640,30 592) code in ITU-T G.975.1 and the classic RS(255,239) code which is widely used in optical transmission systems in ITU-T G.975 at the bit error rate(BER) of 10-7.Therefore,the constructed QC-LDPC(3 780,3 540) code is more suitable for optical transmission systems. 展开更多
关键词 Bit error rate convolutional codes Error correction Inverse problems Light transmission Optical communication Satellite communication systems Transmissions
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Improved Adaptive Random Convolutional Network Coding Algorithm 被引量:2
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作者 Guo Wangmei Cai Ning Wang Xiao 《China Communications》 SCIE CSCD 2012年第11期63-69,共7页
To address the issue of field size in random network coding, we propose an Improved Adaptive Random Convolutional Network Coding (IARCNC) algorithm to considerably reduce the amount of occupied memory. The operation o... To address the issue of field size in random network coding, we propose an Improved Adaptive Random Convolutional Network Coding (IARCNC) algorithm to considerably reduce the amount of occupied memory. The operation of IARCNC is similar to that of Adaptive Random Convolutional Network Coding (ARCNC), with the coefficients of local encoding kernels chosen uniformly at random over a small finite field. The difference is that the length of the local encoding kernels at the nodes used by IARCNC is constrained by the depth; meanwhile, increases until all the related sink nodes can be decoded. This restriction can make the code length distribution more reasonable. Therefore, IARCNC retains the advantages of ARCNC, such as a small decoding delay and partial adaptation to an unknown topology without an early estimation of the field size. In addition, it has its own advantage, that is, a higher reduction in memory use. The simulation and the example show the effectiveness of the proposed algorithm. 展开更多
关键词 convolutional network coding adaptive network coding algorithm random coding
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Construction of type-Ⅱ QC-LDPC codes with fast encoding based on perfect cyclic difference sets 被引量:1
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作者 李玲香 李海兵 +1 位作者 李季碧 江华 《Optoelectronics Letters》 EI 2017年第5期358-362,共5页
In view of the problems that the encoding complexity of quasi-cyclic low-density parity-check(QC-LDPC) codes is high and the minimum distance is not large enough which leads to the degradation of the error-correction ... In view of the problems that the encoding complexity of quasi-cyclic low-density parity-check(QC-LDPC) codes is high and the minimum distance is not large enough which leads to the degradation of the error-correction performance, the new irregular type-Ⅱ QC-LDPC codes based on perfect cyclic difference sets(CDSs) are constructed. The parity check matrices of these type-Ⅱ QC-LDPC codes consist of the zero matrices with weight of 0, the circulant permutation matrices(CPMs) with weight of 1 and the circulant matrices with weight of 2(W2CMs). The introduction of W2CMs in parity check matrices makes it possible to achieve the larger minimum distance which can improve the error-correction performance of the codes. The Tanner graphs of these codes have no girth-4, thus they have the excellent decoding convergence characteristics. In addition, because the parity check matrices have the quasi-dual diagonal structure, the fast encoding algorithm can reduce the encoding complexity effectively. Simulation results show that the new type-Ⅱ QC-LDPC codes can achieve a more excellent error-correction performance and have no error floor phenomenon over the additive white Gaussian noise(AWGN) channel with sum-product algorithm(SPA) iterative decoding. 展开更多
关键词 convolutional codes Encoding (symbols) Error correction Errors Gaussian noise (electronic) Iterative decoding Iterative methods Matrix algebra Satellite communication systems Set theory Signal encoding Turbo codes White noise
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Integrated Joint Source-Channel Symbol-by-Symbol Decoding of Variable-Length Codes Using 3-D MAP Sequence Estimation 被引量:1
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作者 WU Jing CHEN Shuzhen 《Wuhan University Journal of Natural Sciences》 CAS 2007年第3期471-475,共5页
Most of multimedia schemes employ variable-length codes (VLCs) like Huffman code as core components in obtaining high compression rates. However VLC methods are very sensitive to channel noise. The goal of this pape... Most of multimedia schemes employ variable-length codes (VLCs) like Huffman code as core components in obtaining high compression rates. However VLC methods are very sensitive to channel noise. The goal of this paper is to salvage as many data from the damaged packets as possible for higher audiovisual quality. This paper proposes an integrated joint source-channel decoder (I-JSCD) at a symbol-level using three-dimensional (3-D) trellis representation for first-order Markov sources encoded with VLC source code and convolutional channel code. This method combines source code and channel code state-spaces and bit-lengths to construct a two-dimensional (2-D) state-space, and then develops a 3-D trellis and a maximum a-posterior (MAP) algorithm to estimate the source sequence symbol by symbol. Experiment results demonstrate that our method results in significant improvement in decoding performance, it can salvage at least half of (50%) data in any channel error rate, and can provide additional error resilience to VLC stream like image, audio, video stream over high error rate links. 展开更多
关键词 integrated joint source-channel decoding (I-JSCD) variable-length code (VLC) exp-Golomb code convolutional code maximum a-oosteriori (MAP)
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Structured sparsity assisted online convolution sparse coding and its application on weak signature detection 被引量:1
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作者 Huijie MA Shunming LI +2 位作者 Jiantao LU Zongzhen ZHANG Siqi GONG 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2022年第1期266-276,共11页
Due to the strong background noise and the acquisition system noise,the useful characteristics are often difficult to be detected.To solve this problem,sparse coding captures a concise representation of the high-level... Due to the strong background noise and the acquisition system noise,the useful characteristics are often difficult to be detected.To solve this problem,sparse coding captures a concise representation of the high-level features in the signal using the underlying structure of the signal.Recently,an Online Convolutional Sparse Coding(OCSC)denoising algorithm has been proposed.However,it does not consider the structural characteristics of the signal,the sparsity of each iteration is not enough.Therefore,a threshold shrinkage algorithm considering neighborhood sparsity is proposed,and a training strategy from loose to tight is developed to further improve the denoising performance of the algorithm,called Variable Threshold Neighborhood Online Convolution Sparse Coding(VTNOCSC).By embedding the structural sparse threshold shrinkage operator into the process of solving the sparse coefficient and gradually approaching the optimal noise separation point in the training,the signal denoising performance of the algorithm is greatly improved.VTNOCSC is used to process the actual bearing fault signal,the noise interference is successfully reduced and the interest features are more evident.Compared with other existing methods,VTNOCSC has better denoising performance. 展开更多
关键词 Dictionary learning Online convolutional sparse coding(OCSC) Signal denoising Signal processing Weak signature detection
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Improving the Structure of Multiple Dimension Turbo Codes Using Multiple Identical Component Encoders
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作者 WANG Zhenghai1, TIAN Mao1, WANG Yuhao2 1. School of Electronic Information, Wuhan University, Wuhan 430072, Hubei, China 2. School of Information Engineering, Nanchang University, Nanchang 330031, Jiangxi, China 《Wuhan University Journal of Natural Sciences》 CAS 2010年第4期330-334,共5页
In this paper,we propose an improved structure for M-dimension ( M ≥ 2)turbo codes using M identical component encoders. The presented structure only applies single recursive convolutional encoder to encode M interle... In this paper,we propose an improved structure for M-dimension ( M ≥ 2)turbo codes using M identical component encoders. The presented structure only applies single recursive convolutional encoder to encode M interleaved versions of infor-mation sequence and single tail sequence to operate termination. For the commonly used two-dimension (M = 2) turbo codes,two cascade soft input soft output (SISO) decoders are detailed to de-code the corresponding codes. With the two cascade SISO decod-ers,this coding structure obviously outperforms traditional turbo codes at high code rates,especially,about 0.3 dB gain can be ob-tained at code rate 0.9 in additive white Gaussian noise channel with quadrature phase shift keying modulation. This makes the proposed coding structure very attractive for future radio commu-nication systems with high throughput requirements. 展开更多
关键词 turbo codes concatenated codes convolutional codes soft input soft output (SISO)
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Algebraic Approach to Random Convolutional Network Coding over Wireless Packet Networks
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作者 郭网媚 刘斌越 蒋馥蔚 《Transactions of Tianjin University》 EI CAS 2013年第4期307-312,共6页
To characterize the algebraic structure of wireless network coding, a hypergragh is utilized to model wireless packet networks from network layer. The algebraic description of random convolutional network coding is de... To characterize the algebraic structure of wireless network coding, a hypergragh is utilized to model wireless packet networks from network layer. The algebraic description of random convolutional network coding is deduced, and the coding condition is also presented. Analyses and simulations show that random convolutional coding is capacity-achieving with probability approaching 1. 展开更多
关键词 wireless network coding random convolutional network coding HYPERGRAPH capacity-achieving
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A multiple copyright identification watermarking algorithm based on code division multiple access
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作者 张帆 li Jie +1 位作者 Su Yuting Zhang Chuntian 《High Technology Letters》 EI CAS 2008年第4期377-383,共7页
A multiple watermarking algorithm is presented according to the multiple accessing technique of the code division multiple access (CDMA) system. Multiple watermarks are embedded into digital images in the wavelet tr... A multiple watermarking algorithm is presented according to the multiple accessing technique of the code division multiple access (CDMA) system. Multiple watermarks are embedded into digital images in the wavelet transform domain. Each of the watermarks is embedded and extracted independently without impacts to each other. Multiple watermarks are convolution encoded and block interleaved, and the orthogonal Gold sequences are used to spread spectrum of the copyright messages. CDMA encoded water-mark messages are embedded into the wavelet sub-bands excluding the wavelet HH1 sub-bands. The embedment amplitude is decided by Watson' s perceptual model of wavelet transform domain, and the embedmeut position in the selected wavelet sub-bands is decided randomly by a pseudo-random noise (PN) sequence. As a blind watermm'king algorithm, watermarks are extracted without original image. The watermarking capacity of proposed algorithm is also discussed. When two watermarks are embedded in an image at the same time, the capacity is larger than the capacity when a single watermark is embedded, and is smaller than the sum of the capacity of two separately embedded watermarks. Experimental results show that the proposed algorithm improves the detection bits error rate (BER) observably, and the multiple watermarks have a preferable robustness and invisibility. 展开更多
关键词 code division multiple access (CDMA) WATERMARKING convolutional coding
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Joint Source-Channel Bit Allocation Based on Expected End-to-End Distortion Model 被引量:1
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作者 马汉杰 陈耀武 《Journal of Donghua University(English Edition)》 EI CAS 2010年第4期458-462,共5页
An adaptive joint source channel bit allocation method for video communications over error-prone channel is proposed.To protect the bit-streams from the channel bit errors,the rate compatible punctured convolution(RCP... An adaptive joint source channel bit allocation method for video communications over error-prone channel is proposed.To protect the bit-streams from the channel bit errors,the rate compatible punctured convolution(RCPC)code is used to produce coding rates varying from 4/5 to 1/2 using the same encoder and the Viterbi decoder.An expected end-to-end distortion model was presented to estimate the distortion introduced in compressed source coding due to quantization and channel bit errors jointly.Based on the proposed end-to-end distortion model,an adaptive joint source-channel bit allocation method was proposed under time-varying error-prone channel conditions.Simulated results show that the proposed methods could utilize the available channel capacity more efficiently and achieve better video quality than the other fixed coding-based bit allocation methods when transmitting over error-prone channels. 展开更多
关键词 joint source-channel coding end-to-end distortion bit allocation rate compatible punctured convolution code
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