Application of Maxeler DataFlow Supercomputing to Spherical Code Design

An algorithm for spherical code design, based on the variable repulsion force method is presented. The iterative nature of the algorithm and the large number of operations it performs make it suitable for implementation on dataflow supercomputing devices. Gains in computation speed and power consumption of such an implementation are given. Achieved minimum distances and simulated error probabilities of obtained codes are presented.

[1]  Achill Schürmann,et al.  Experimental Study of Energy-Minimizing Point Configurations on Spheres , 2009, Exp. Math..

[2]  Carlos R. P. Hartmann,et al.  Iteratively maximum likelihood decodable spherical codes and a method for their construction , 1988, IEEE Trans. Inf. Theory.

[3]  John K. Karlof.  Decoding spherical codes for the Gaussian channel , 1993, IEEE Trans. Inf. Theory.

[4]  Edward De Bono,et al.  Serious Creativity: Using the Power of Lateral Thinking to Create New Ideas , 1992 .

[5]  Veljko M. Milutinovic,et al.  Comparing Controlflow and Dataflow for Tensor Calculus: Speed, Power, Complexity, and MTBF , 2018, ISC Workshops.

[6]  Prof. Dr. Veljko Milutinovic,et al.  DataFlow Supercomputing Essentials , 2017, Computer Communications and Networks.

[7]  David Silverstein,et al.  Insourcing Innovation: How to Achieve Competitive Excellence Using TRIZ , 2007 .

[8]  D. Lazi.  Class of block codes for the Gaussian channel , 1980 .

[9]  Jeffrey Wang.  Finding and Investigating Exact Spherical Codes , 2009, Exp. Math..

[10]  T. Tarnai,et al.  Improved packing of equal circles on a sphere and rigidity of its graph , 1983, Mathematical Proceedings of the Cambridge Philosophical Society.

[11]  Henry Cohn,et al.  Universally optimal distribution of points on spheres , 2006, math/0607446.

[12]  Tony Buzan,et al.  Use Your Head , 1974 .

[13]  Eiichi Bannai,et al.  Uniqueness of Certain Spherical Codes , 1981, Canadian Journal of Mathematics.

[14]  Michael A. Orloff,et al.  Inventive Thinking through TRIZ: A Practical Guide , 2006 .

[15]  Henry Cohn,et al.  Uniqueness of the (22,891,1/4) spherical code , 2006, math/0607448.

[16]  Oleg R. Musin,et al.  The Tammes Problem for N = 14 , 2014, Exp. Math..

[17]  Jon Hamkins,et al.  Asymptotically dense spherical codes - Part II: Laminated spherical codes , 1997, IEEE Trans. Inf. Theory.

[18]  Veljko M. Milutinovic,et al.  Chapter One - A Systematic Approach to Generation of New Ideas for PhD Research in Computing , 2017, Adv. Comput..

[19]  S. Torquato,et al.  Rigidity of Spherical Codes , 2011, 1102.5060.

[20]  A. G. Burr.  Spherical codes for M-ary code shift keying , 1989 .

[21]  Jon Hamkins,et al.  Asymptotically dense spherical codes - Part h Wrapped spherical codes , 1997, IEEE Trans. Inf. Theory.

[22]  D. Kottwitz.  The densest packing of equal circles on a sphere , 1991 .

[23]  David L. Kepert,et al.  The optimal packing of circles on a sphere , 1991 .

[24]  N. J. A. Sloane,et al.  Tables of sphere packings and spherical codes , 1981, IEEE Trans. Inf. Theory.

[25]  Semyon Savransky,et al.  Engineering of Creativity: Introduction to TRIZ Methodology of Inventive Problem Solving , 2000 .

[26]  Oleg R. Musin,et al.  The Strong Thirteen Spheres Problem , 2010, Discret. Comput. Geom..

[27]  Jon Hamkins,et al.  Gaussian source coding with spherical codes , 2002, IEEE Trans. Inf. Theory.

[28]  Alexey A. Glazyrin,et al.  Stability of optimal spherical codes , 2017, ArXiv.

[29]  Veljko M. Milutinovic,et al.  FPGA accelerator for floating-point matrix multiplication , 2012, IET Comput. Digit. Tech..

[30]  Vivek K. Goyal,et al.  On concentric spherical codes and permutation codes with multiple initial codewords , 2009, 2009 IEEE International Symposium on Information Theory.

[31]  Christine Bachoc,et al.  Optimality and uniqueness of the (4, 10, 1/6) spherical code , 2007, J. Comb. Theory, Ser. A.

[32]  J. Lindner,et al.  On The Construction of Non-coherent Space Time Codes from High-dimensional Spherical Codes , 2006, 2006 IEEE Ninth International Symposium on Spread Spectrum Techniques and Applications.