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An efficient approach to lattice-based fixed-rate entropy-coded vector quantization

EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS 2003年第2期14卷 141-147页

作者： Nikneshan, S Khandani, AK Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

In the absence of channel noise, variable-length quantizers perform better than fixed-rate Lloyd-Max quantizers for any source with a non-uniform density function. However, channel errors can lead to a loss of synchronization resulting in a propagation of error. To avoid having variable rate, one can use a vector quantizer selected as a sub-set of high probability points in the Cartesian product of a set of scalar quantizers and represent its elements with binary code-words of the same length (quantizer shaping). We choose these elements from a lattice, resulting in a higher quantization gain in comparison to simply using the Cartesian product of a set of scalar quantizers. We introduce a class of lattices which have a low encoding complexity, and at the same time result in a noticeable quantization gain. We combine the procedure of lattice encoding with that of quantizer shaping using hierarchical dynamic programming. In addition, by devising appropriate partitioning and merging rules, we obtain sub-optimum schemes of low complexity and small performance degradation. The proposed methods show a substantial improvement in performance and/or a reduction in the complexity with respect to the best known results. Copyright (C) 2003 AEI.

关键词： Elements crystal lattices quantizer degradation of performance Entropy coding Cartesian product Vector quantization encoding complexity

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PKC-PC: A variant of the McEliece public-key cryptosystem based on polar codes

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IET COMMUNICATIONS 2020年第12期14卷 1883-1893页

作者： Hooshmand, Reza Koochak Shooshtari, Masoumeh Reza Aref, Mohammad Shahid Sattari Aeronaut Univ Sci & Technol Dept Elect Engn Tehran Iran Sharif Univ Technol Dept Elect Engn Tehran Iran

Polar codes are novel and efficient error-correcting codes with low encoding and decoding complexities. These codes have a channel-dependent generator matrix, which is determined by the code dimension, code length and transmission channel parameters. A variant of the McEliece public-key cryptosystem based on polar codes, called the PKC-PC, is studied. Since the structure of the polar codes' generator matrix depends on the parameters of the channel, the authors have used an efficient approach to conceal their generator matrix. The proposed approach is based on a random selection of rows of the matrix by which a random generator matrix is constructed. Using the characteristics of polar codes and introducing an efficient approach, they could reduce the public and secret key sizes, and computational complexity compared to the McEliece cryptosystem. Moreover, they show that PKC-PC yields an increased security level against conventional attacks as well as possible vulnerabilities to the code-based public-key cryptosystems. Furthermore, they prove the security of the authors' cryptosystem and show that its security is reduced to solve NP-complete problems, called polar parameterised syndrome decoding and polar parameterised codeword existence.

关键词： public key cryptography decoding error correction codes computational complexity polar codes channel coding matrix algebra PKC-PC McEliece public-key cryptosystem polar codes error-correcting codes channel-dependent generator matrix code dimension code length transmission channel parameters random generator matrix public key sizes secret key sizes code-based public-key cryptosystems polar parameterised syndrome decoding decoding complexity encoding complexity computational complexity polar parameterised codeword existence

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Decoding performance analysis of good-channel relaxed polar codes with 3 x 3 kernel matrix

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IET COMMUNICATIONS 2019年第8期13卷 1131-1139页

作者： Cao, Yang Zhang, Han Tu, Qiaoling Chongqing Univ Technol Dept Elect & Elect Engn Chongqing 400054 Peoples R China

Relaxed polar codes are proposed to reduce the encoding and decoding complexity of polar codes. The original relaxed polar codes are based on 2 x 2 kernel matrices, but polar codes with 3 x 3 kernel matrices are expected to achieve better error performance. So, in this work, the authors extended relaxed polar codes to N = 3(n) case. Different from 2 x 2 kernel matrices, there are several choices for 3 x 3 kernel matrices. So, they classified 3 x 3 kernel matrices into three categories and derived transformation formulas of their Bhattacharyya parameters. Based on the formulas, they proved that the proposed relaxed polar codes had better error performance than the corresponding fully polarised codes when successive cancellation decoder was adopted. To estimate the complexity reduction, upper and lower bounds on complexity reduction of the proposed relaxed polar codes were provided. For the kernel selection, size relationship of complexity reduction of the proposed relaxed polar codes with different kernels were analysed. Results showed that relaxed polar codes with different matrices had their own characters and can be used in different channel and polarisation condition. Simulation results show that, with proper selection of matrices, the proposed relaxed polar codes can reduce more complexity and bring more coding gain.

关键词： channel coding decoding polar codes good-channel relaxed polar codes kernel matrix encoding complexity decoding complexity Bhattacharyya parameters

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MULTIDIMENSIONAL SIGNAL SETS THROUGH THE SHELL CONSTRUCTION FOR PARALLEL CHANNELS

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IEEE TRANSACTIONS ON COMMUNICATIONS 1992年第3期40卷 500-512页

作者： FORTIER, P RUIZ, A CIOFFI, JM STANFORD UNIV DEPT ELECT ENGNINFORMAT SYST LABSTANFORDCA 94305 IBM CORP THOMAS J WATSON RES CTRHAWTHORNENY 10532

The design of efficient multidimensional signal sets has gained importance with the development of coset codes. We derive a procedure to send r bits on M parallel channels. A decomposition of the best constellation in Z(M) + (1/2,..., 1/2) is given in terms of the cross-products of lower dimensional shells of points. The proposed scheme can be used with good known coset codes to provide an alternate method of coded modulation. Our results indicate that we can get good shaping gains for low encoder complexity. The method is also generalized for channels with unequal gains. We also find a significant performance advantage at fixed shaping gain, in certain cases, with respect to the recent Voronoi Constellations in terms of peak-to-average power and constellation expansion.

关键词： Writers MULTIDIMENSIONAL containment structure parallel channel inequalities Parallel Lines CONSTELLATIONS average power modulation coding encoding complexity

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Practical analysis of codebook design and frequency offset estimation for virtual-multiple-input-multiple-output systems

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IET COMMUNICATIONS 2013年第6期7卷 585-594页

作者： Jiang, Jing Thompson, John S. Sun, Hongjian Grant, Peter M. Univ Surrey Ctr Commun Syst Res Guildford GU2 7XH Surrey England Univ Edinburgh Sch Engn Inst Digital Commun Edinburgh EH9 3JL Midlothian Scotland Kings Coll London Dept Elect Engn London WC2R 2LS England

A virtual-multiple-input-multiple-output (MIMO) wireless system using the receiver-side cooperation with the compress-and-forward (CF) protocol, is an alternative to a point-to-point MIMO system, when a single receiver is not equipped with multiple antennas. It is evident that the practicality of CF cooperation will be greatly enhanced if an efficient source coding technique can be used at the relay. It is even more desirable that CF cooperation should not be unduly sensitive to carrier frequency offsets (CFOs). This study presents a practical study of these two issues. Firstly, codebook designs of the Voronoi vector quantisation (VQ) and the tree-structure VQ (TSVQ) to enable CF cooperation at the relay are described. A comparison in terms of the codebook design and encoding complexity is analysed. It is shown that the TSVQ is much simpler to design and operate, and can achieve a favourable performance-complexity tradeoff. Furthermore, this study demonstrates that CFO can lead to significant performance degradation for the virtual-MIMO system. To overcome this, it is proposed to maintain clock synchronisation and jointly estimate the CFO between the relay and the destination. This approach is shown to provide a significant performance improvement.

关键词： communication complexity computational geometry diversity reception frequency estimation MIMO communication protocols radio receivers source coding synchronisation trees (mathematics) vector quantisation cooperative communication relay networks (telecommunication) communication complexity computational geometry diversity reception frequency estimation MIMO communication protocols radio receivers source coding synchronisation trees (mathematics) vector quantisation cooperative communication relay networks (telecommunication) clock synchronisation virtual MIMO system CFO performance complexity tradeoff TSVQ encoding complexity tree structure VQ Voronoi vector quantisation carrier frequency offset relay source coding technique CF cooperation point-to-point MIMO wireless system compress and forward protocol receiver side cooperation frequency offset estimation codebook design multiple input multiple output

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AN EFFICIENT complexity REDUCTION ALGORITHM FOR CU SIZE DECISION IN HEVC

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INTERNATIONAL JOURNAL OF INNOVATIVE COMPUTING INFORMATION AND CONTROL 2018年第1期14卷 309-322页

作者： Jiang, Xiantao Wang, Xiaofeng Song, Tian Shi, Wen Katayama, Takafumi Shimamoto, Takashi Leu, Jenq-Shiou Shanghai Maritime Univ Dept Informat Engn 1550 Harbour RdHaigang Ave Shanghai 201306 Peoples R China Tokushima Univ Dept Elect & Elect Engn 2-24 Shinkura Cho Tokushima 7708501 Japan Natl Taiwan Univ Sci & Technol Dept Elect & Comp Engn 43Keelung RdSec 4 Taipei 10607 Taiwan

In brief, this work focuses on reducing the encoding complexity with less than 1% encoding efficiency loss for low delay (LD) and random access (RA) profiles in HEVC. An efficient CU (coding unit) size decision algorithm based on probabilistic graphical models is proposed for HEVC inter coding, which contains two methods: the CU size early termination (CUET) decision method and the CU size early skip (CUES) decision method. The CU pruning is modeled as a binary classification problem based on the Naive Bayes (NB) model. Furthermore, a Markov random fields (MRF) model based method is presented to improve the algorithm performance. The difference from previous works is that residual flag in inter-coded CU and the neighboring information are used to determine the CU size. The offline learning method is used to obtain the statistical parameters. This presented approach can significantly reduce the encoding complexity. Furthermore, it can bring lower power cost for hardware implementation. The simulation experiment results demonstrate that this method can significantly reduce by 50.59% and 53.86% average encoding complexity under low delay and random access profiles, while the encoding efficiency can be reduced by 0.82% and 0.98% on average. Moreover, the rate-distortion (RD) performance of this method is nearly the same as HEVC reference software.

关键词： Video coding CU size encoding efficiency encoding complexity

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New encoding scheme of polar codes

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The Journal of China Universities of Posts and Telecommunications 2013年第1期20卷 91-94页

作者： WANG Jun-xuan ZHANG Yan-yan School of Communication and Information Engineering Xi'an University of Posts and Telecommunications

The ＇polar coding＇ proposed by Dr. Ankan can achieve channels （B-DMC）. The generator matrix of polar codes is the symmetric capacity of binary-input discrete memoryless Gu = BuF^n for N=2n, BN was a permutation matrix. In the article it was realized with an interleaver, so the matrix production of GN was avoided; then the generator matrix was just determined by the matrix F^n which was constructed with three sub-matrixes of F^n-1 and one 2^N-1 order zero matrix, it was deal with fast Hadamard transform （FHT） algorithm. The complexity of the new scheme was reduced sharply, and an iterative algorithm also can be used. The example showed that when N=8, complexity of the encoding scheme was just 16 which is obviously less than that of original encoding scheme 36.

关键词： polar codes fast Hadamard translation (FHT) encoding complexity

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HEVC fast reference picture selection

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ELECTRONICS LETTERS 2015年第25期51卷 2109-2110页

作者： Yang, Shih-Hsuan Huang, Kai-Sheng Natl Taipei Univ Technol Comp Sci & Informat Engn Taipei 10608 Taiwan

The new high efficiency video coding (HEVC) standard facilitates the realisation of ultrahigh-definition video applications. Although the compression efficiency of the HEVC standard is double that of the well-established H.264 standard, HEVC incurs a considerably higher encoding complexity. This Letter presents an algorithm aimed at expediting reference picture selection processes in HEVC encoding. The proposed algorithm is primarily based on a reference picture and block discovered using the advanced motion vector prediction (AMVP) algorithm. Two acceleration conditions are included in the proposed algorithm. The first early-decision condition entails examining the rate-distortion (RD) cost associated with AMVP, and if this cost is lower than a predefined threshold, motion estimation is confined to the AMVP-selected reference picture. Furthermore, for coding units of size 64 x 64 (N = 32) with a prediction-unit (PU) partitioning of 2N x N or N x 2N, the second PU uses the same reference picture as the first PU if the first PU satisfies the first early-decision condition. The experimental results revealed that the proposed algorithm considerably reduced the total encoding time with negligible RD degradation.

关键词： motion estimation video coding AMVP algorithm H.264 standard HEVC fast reference picture selection process advanced motion vector prediction algorithm encoding complexity high efficiency video coding standard motion estimation prediction-unit partitioning rate-distortion cost

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Fast QTMT decision tree for Versatile Video Coding based on deep neural network

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MULTIMEDIA TOOLS AND APPLICATIONS 2022年第29期81卷 42731-42747页

作者： Abdallah, Bouthaina Belghith, Fatma Ben Ayed, Mohamed Ali Masmoudi, Nouri Univ Sfax Natl Engn Sch Sfax Elect & Informat Technol Lab Sfax 3035 Tunisia Univ Sfax Sfax Natl Sch Elect & Commun ENETCOM New Technol & Telecom Syst Lab NTSCOM Sfax Tunisia

Versatile Video Coding (VVC), the emerging video coding standard, outperforms the coding efficiency of the previous standard named High Efficiency Video Coding (HEVC) at the cost of an encoding complexity increase. In fact, VVC proposes a new partitioning block structure called quadtree with nested multi-type tree (QTMT) that introduces a more flexible partition shape compared to the previous splitting algorithms namely quadtree plus binary tree (QTBT) and quadtree (QT) structures adopted in HEVC. However, QTMT increases the encoding time due to the rate-distortion cost (RDcost) process. In order to overcome this issue, this paper proposes a fast intra partitioning algorithm based on a Deep Learning (DL) approach using a Convolution Neural Network (CNN). First, a fast QTMT partition algorithm based on a CNN-binary tree horizontal (CNN-BTH) network is developed to predict the BTH mode decision at 32x32 Coding Units (CUs). The BTV decision tree algorithm is also predicted at this level by a CNN-binary tree vertical (CNN-BTV). Then, two algorithms are combined to suggest a new fast intra QTMT decision tree algorithm. Compared to the VVC reference software VTM-3.0, the proposed overall intra QTMT partition approach reaches a significant complexity reduction down to 37% compared to the original software VTM-3.0, and an average of 31% in terms of encoding time saving with a slight loss in coding performance.

关键词： Versatile Video Coding (VVC) encoding complexity Quadtree with nested multi-type tree (QTMT) Convolution Neural Network (CNN)

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The complexity of Network Coding With Two Unit-Rate Multicast Sessions

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IEEE TRANSACTIONS ON INFORMATION THEORY 2013年第9期59卷 5692-5707页

作者： Song, Wentu Cai, Kai Feng, Rongquan Yuen, Chau Peking Univ LMAM Sch Math Sci Beijing Peoples R China Singapore Univ Technol & Design Singapore Singapore Chinese Univ Hong Kong Inst Network Coding Shatin Hong Kong Peoples R China

The encoding complexity of network coding for single multicast networks has been intensively studied from several aspects: e. g., the time complexity, the required number of encoding links, and the required field size for a linear code solution. However, these issues as well as the solvability are less understood for networks with multiple multicast sessions. Recently, Wang and Shroff showed that the solvability of networks with two unit-rate multicast sessions (2-URMS) can be decided in polynomial time [4]. In this paper, we prove that for the 2-URMS networks: 1) the solvability can be determined with time O(vertical bar E vertical bar);2) a solution can be constructed with time (vertical bar E vertical bar);3) an optimal solution can be obtained in polynomial time;4) the number of encoding links required to achieve a solution is upper-bounded by max {3, 2N-2};and 5) the field size required to achieve a linear solution is upper-bounded by, max {2, left perpendicular root 2N - 7/4 + 1/2right perpendicular}, where vertical bar E vertical bar is the number of links and is the number of sinks of the underlying network. Both bounds are shown to be tight.

关键词： encoding complexity network coding region decomposition

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