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IEEE Global Communications Conference (GLOBECOM) on Advanced Technology for 5G Plus

作者： Zou, Jun Shum, Kenneth W. Sung, Chi Wan Nanjing Univ Sci & Technol Sch Elect & Opt Engn Nanjing Peoples R China City Univ Hong Kong Dept Elect Engn Hong Kong Peoples R China Chinese Univ Hong Kong Shenzhen Sch Sci & Engn Shenzhen Peoples R China

ISBN: (纸本)9781728182988

A novel non-orthogonal multiple access (NOMA) scheme with spherical code superposition and its user pairing strategy are proposed. A transmitter transmits the superposition of the signals of two users, each of which is selected from the high dimensional spherical code on the same time-frequency resource by power-domain multiplexing NOMA. Upper bounds of the word error probabilities of the two users are derived. Based on them, a power allocation scheme for the two users is proposed, which guarantees that their word error probabilities are below a certain threshold. Under our power allocation scheme, the optimal user pairing strategy that minimizes the total power consumption in a general multi-user system is analytically found. Numerical results show that our proposed system outperforms some benchmark methods.

关键词： Non-orthogonal multiple access (NOMA) spherical code user pairing

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Index Modulation Based on Four-Dimensional spherical code and Its DNN-Based Receiver Design

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2021年第12期70卷 13401-13405页

作者： Zou, Jun Qu, Jing Guo, Yirui Liu, Guangzu Shu, Feng Nanjing Univ Sci & Technol Sch Elect & Opt Engn Nanjing 210094 Peoples R China Hainan Univ Sch Informat & Commun Engn Haikou 570228 Hainan Peoples R China

A novel index modulation with spherical code and its constellation mapping are proposed. We derive the closed form of the approximation bound of the bit error rate (BER) of the OFDM-IM system based on four-dimensional spherical code. Our derived BER is very close to the simulation results. And different constellation mapping method have different BER performance and the gap is less than 0.2 dB. To reduce the detection complexity which is caused by the high-dimensional modulation, a DNN-based receiver with partial-connected layer is proposed. Simulation results show that our proposed DNN-based receiver can greatly reduce the complexity while its BER performance is close to the classical maximum likelihood detection method.

关键词： Modulation Indexes codes Bit error rate Receivers Complexity theory OFDM Index modulation spherical code deep neural network

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Index Modulation Based on Four-dimensional spherical code 3

Index Modulation Based on Four-dimensional Spherical Code

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3rd IEEE International Conference on Information Communication and Signal Processing (ICICSP)

作者： Qu, Jing Zou, Jun Sun, Jiyuan Li, Meng Xu, Chen Nanjing Univ Sci & Technol Nanjing Peoples R China

ISBN: (数字)9781728188232

ISBN: (纸本)9781728188232

In this paper, we propose an orthogonal frequency division multiplexing with index modulation (OFDM-IM) based on high-dimensional spherical codes. Unlike the traditional OFDM-IM system, which conveys the traditional M-ary constellation symbol on the active subcarriers, we use the adjacent subcarriers in the sub-block as a whole to be modulated based on high dimensional spherical code. Since the Euclidean distances between the constellation points increase by using high dimensional modulation, the performance of the OFDM-IM system is improved. We derive the general form of symbol error rate (SER) for the proposed OFDM-IM system with the maximum likelihood (ML) detection. The simulation results show that the bit error rate (BER) and SER of our proposed scheme is better than that of the traditional OFDM-IM system. We also investigate the effect of channel estimation error on our proposed scheme.

关键词： OFDM Index modulation spherical code maximum likelihood detection

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OTFS-IM Modulation Based on Four-Dimensional spherical code in Air-to-Ground Communication

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DRONES 2023年第10期7卷

作者： Gu, Peng Guo, Lin Jin, Shen Liu, Guangzu Zou, Jun Nanjing Univ Sci & Technol Sch Elect & Opt Engn Nanjing 210094 Peoples R China State Grid Jibei Informat & Telecommun Co Beijing 100053 Peoples R China

Unmanned aerial vehicles (UAVs) have been widely utilized for their various advantages. However, UAVs exhibit high mobility and energy storage restrictions in some applications, which can compromise the quality and reliability of communication links. This is a challenge that future aircraft and low-orbit aircraft will inevitably encounter. To effectively address the issue of dynamic Doppler spread in air-to-ground communication, this paper creatively introduces four-dimensional spherical code modulation into the orthogonal time-frequency space with an index modulation (OTFS-IM) system. The fundamental concept of the four-dimensional spherical code is elaborated in detail. Multiple resource symbols can be jointly used to increase the modulation dimension, thereby achieving a larger minimum Euclidean distance between constellation points. Furthermore, detailed analysis is conducted on the bit error rate (BER) and the peak-to-average-power ratio (PAPR) expressions of the proposed system to evaluate its performance and provide theoretical guidance. The proposed scheme not only adapts well to high-speed scenarios but also achieves better power consumption efficiency. The simulation results demonstrate that our proposed scheme outperforms conventional methods. Its robustness and generalization ability are also validated.

关键词： orthogonal time-frequency space index modulation spherical code maximum likelihood detection

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spherical codes With Prescribed Signed Permutation Automorphisms Inside Shells of Low-Dimensional Integer Lattices

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IEEE TRANSACTIONS ON INFORMATION THEORY 2024年第12期70卷 8669-8674页

作者： Ganzhinov, Mikhail Ostergard, Patric R. J. Aalto Univ Dept Informat & Commun Engn Sch Elect Engn Aalto 00076 Finland

Let S( n, t, k) be the maximum size of a code containing only vectors of the kth shell of the integer lattice Zn such that the inner product between distinct vectors does not exceed t. In this paper we compute lower bounds for S( n, t, k) for small values of n, t and k by carrying out computer searches for codes with prescribed automorphisms. We prescribe groups of signed permutation automorphisms acting transitively on the pairs of coordinates and coordinate values as well as other closely related groups of automorphisms. Several of the constructed codes lead to improved lower bounds for spherical codes.

关键词： Automorphism group spherical code integer lattice

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Simulation of magnetic resonance static powder lineshapes: A quantitative assessment of spherical codes

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JOURNAL OF MAGNETIC RESONANCE 1999年第2期138卷 288-297页

作者： Ponti, A CNR Ctr Studio Relaz Struttura & Reatt Chim I-20133 Milan Italy

Simulation of magnetic resonance static powder spectra is performed by a (possibly weighted) summation of single-crystal spectra computed for different orientations of the external field with respect to the principal axes of the magnetic interactions. The many available methods differ in the choice of the integration points (i.e., orientations) and weights, the set of which is called spherical code. There is continuing interest in minimizing the number of integration points necessary to a good simulation. Neglecting the possible interpolation of transition frequencies and intensities between integration points, we turn our attention to the efficiency of spherical codes themselves. To this end, an unbiased quantitative procedure to assess their efficiency in simulating magnetic resonance static powder spectra is proposed. To achieve an impartial judgement, the procedure has been designed by carefully taking into consideration the following points: choice of exact reference spectra;accurate definition of the merit figures;extended range of number of integration points;orientation dependence of the efficiency. The proposed procedure has been applied to an inclusive set of 23 spherical codes. It was found that most codes perform rather similarly. SPIRAL is the most efficient code, whereas Monte Carlo and "repulsive" codes show the best rotational invariance of the simulated lineshape with respect to the orientation of the spherical code. (C) 1999 Academic Press.

关键词： spectral simulation static powder lineshape spherical code

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Few-cosine spherical codes and Barnes-Wall lattices

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JOURNAL OF COMBINATORIAL THEORY SERIES A 2008年第7期115卷 1211-1234页

作者： Griess, Robert L., Jr. Univ Michigan Dept Math Ann Arbor MI 48109 USA

Using Barnes-Wall lattices and 1-cocycles on finite groups of monomial matrices, we give a procedure to construct tricosine spherical codes. This was inspired by a 14-dimensional code which Ballinger, Cohn, Giansiracusa and Morris discovered in studies of the universally optimal property. Their code has 64 vectors -3/7, -1/7, 1/7. We construct the Optimism code,a 4-cosine spherical code with 256 unit vectors in 16-dimensions. The cosines are 0, +/- 1/4, -1. Its automorphism group has shape 2(1+8) center dot GL(4, 2). The Optimism code contains a subcode related to the BCGM code. The Optimism code implies existence of a nonlinear binary code with parameters (16, 256, 6), a Nordstrom-Robinson code, and gives a context for determining its automorphism group, which has form 2(4):Alt(7). (C) 2008 Elsevier Inc. All rights reserved.

关键词： finite groups group extension cohomology cocycle spherical code binary code tricosine Barnes-Wall lattice universally optimal property association scheme bolt-room-wall group

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A Minimax Optimization Approach to the spherical codes Problem 4

A Minimax Optimization Approach to the Spherical Codes Probl...

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4th IEEE International Women in Engineering (WIE) Conference on Electrical and Computer Engineering (IEEE WIECON-ECE)

作者： Homsup, Nathawut Homsup, Nuttaka Univ Cent Florida Dept Elect & Comp Engn Orlando FL 32816 USA Kasetsart Univ Dept Elect Engn Bangkok Thailand

ISBN: (纸本)9781728119786

A spherical code with parameter (n, N, gamma) is a set of N points on the unit sphere in n dimension for which the dot product of unit vectors from the origin to any two points is less than or equal to gamma. If each point on the unit sphere is treated as an electron, one approach to this spherical code problem is to define an electrostatic energy of electrons and to optimize for minimum energy. A configuration with minimum energy corresponds to a useful spherical code, but may not be the global minimum solution. Thus, minimizing the energy function does not always minimize gamma. A global solution for the spherical code problem for most of parameters (n, N) is unknown, especially for spherical codes in higher dimension. In this paper, a minimax optimization approach for obtaining spherical codes is analyzed. In this paper, four algorithms are proposed to solve the spherical code problem. The first algorithm is implemented using linear programming with trust region. The second is based on the introduction of the energy function. The third algorithm is based on minimizing the maximum of the dot product of any pairs of unit vectors and the last algorithm is based on the Groebner Bases. By running simulation with these algorithms, configurations for many of the best known spherical codes found in literature were obtained.

关键词： spherical code optimization sphere stereographic projection dot product

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ASYMPTOTIC OPTIMALITY OF MODIFIED spherical codeS WITH SCALAR QUANTIZATION OF GAIN FOR MEMORYLESS GAUSSIAN SOURCES

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1993年第9期E76A卷 1403-1410页

作者： KOGA, H ARIMOTO, S Univ of Tokyo Tokyo Japan

This paper characterizes a class of optimal fixed-to-fixed length data compression codes for memoryless Gaussian sources that achieve asymptotically the rate-distortion bound under squared-error criterion. Any source output of blocklength n is encoded by two steps, i.e., 1) to quantize in gain by scholar quantizers and 2) to quantize in shape by pointsets on n-dimensional hyperspheres. To show the asymptotic optimality of the proposed codes, rate-distortion properties of the codes are analyzed in detail by using a random coding argument on the n-dimensional unit hypersphere. It is shown that asymptotic behaviors of the proposed codes are mainly determined by the choice of scalar quantizer of the gain. As a results, deep insights into not only the class of asymptotically optimal codes but also the rate-distortion bound itself are obtained.

关键词： DATA COMPRESSION GAUSSIAN SOURCE spherical code

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Unitary designs and codes

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DESIGNS codeS AND CRYPTOGRAPHY 2009年第1期53卷 13-31页

作者： Roy, Aidan Scott, A. J. Univ Calgary Dept Math & Stat Inst Quantum Informat Sci Calgary AB T2N 1N4 Canada Griffith Univ Ctr Quantum Dynam Ctr Quantum Comp Technol Brisbane Qld 4111 Australia

A unitary design is a collection of unitary matrices that approximate the entire unitary group, much like a spherical design approximates the entire unit sphere. In this paper, we use irreducible representations of the unitary group to find a general lower bound on the size of a unitary t-design in U(d), for any d and t. We also introduce the notion of a unitary code-a subset of U(d) in which the trace inner product of any pair of matrices is restricted to only a small number of distinct absolute values-and give an upper bound for the size of a code with s inner product values in U(d), for any d and s. These bounds can be strengthened when the particular inner product values that occur in the code or design are known. Finally, we describe some constructions of designs: we give an upper bound on the size of the smallest weighted unitary t-design in U(d), and we catalogue some t-designs that arise from finite groups.

关键词： Unitary design Unitary code Unitary group Rank bound Linear programming bound Delsarte bound spherical design spherical code Quantum process tomography Zonal polynomial

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