Models of optimum discrete signals on the ring combinatorial configurations
DOI:
https://doi.org/10.20535/RADAP.2016.64.10-22Keywords:
discrete signal, code sequence, correcting ability, optimal cyclic code, circular symmetry, optimum principle of structural relations, synthesis of optimal signalsAbstract
The innovative techniques for improving the quality indices of radio-signals for communications and radars with non-uniform structure (e.g. code sequences) with respect to error protection, using novel combinatorial configurations such as cyclic difference sets and Ideal Ring Bundles (IRB)s was regarded. Method for construction of optimum discrete signals, based on these models is proposed. IRBs are cyclic sequences of positive integers, which form perfect partitions of a finite interval [1,N]. The sums of connected sub-sequences of an IRB enumerate the set of integers [1,N-1] exactly R-times. This property makes IRBs useful in applications, which need to partition sets with the smallest possible number of intersections. The models of optimum discrete signals, having previously unknown favorable property, which hold for the same set of the IRBs in varieties permutations of its terms, named the "Glory to Ukraine Stars” have been indicated as a cluster of combinatorial configurations. Some algorithms and useful examples for constructing of optimum cyclic error-correcting codes presented. It shows that remarkable properties of IRBs have encoded in fine structure of circular symmetry and asymmetry ensembles. There are great classes of new two- and multidimensional IRBs, which being in excess classic models of optimum discrete signals with respect to number and combinatorial varieties. Indicate that the IRBs to be in exceed of classic perfect difference sets multiply.References
Перелік посилань
Singer J. A theorem in finite projective geometry and some applications to number theory / J. Singer // Transactions of American Mathematical Society. – 1938. – Vol.43, No.3. – pp. 377-385. doi: 10.1007/BFb0067359.
Hall М. Jr. Combinatorial Theory / M. Jr. Hall. – Blaisell Publishing Company, 1967. – 470 p.
Riznyk V. V. Researches and Applications of the Combinatorial Configurations for Innovative Devices and Process Engineering / V. V. Riznyk, S. W. Golomb ; CRDF Cooperative Grants Program. – Los Angeles, CA 90089-2565, US, 1996. - 10 p.
А.с. СССР 429276 МПК G 01f 11/00 Способ дозирования веществ / В. В. Ризнык, заявл. 12.06.72; опубл. 25.05.74., Бюл. № 19.
Ризнык В.В. Об одном способе оптимального построения дискретных систем / В. В. Ризнык // Электроника и моделирование. – 1975. – Вып. 8. – С.12-15.
Ризнык В. В. Идеальные кольцевые отношения и возможности их практического использования / В. В. Ризнык // Автоматика. – 1981. – №3. – с. 87-90.
Різник В. В. Синтез оптимальних комбінаторних систем / В. В. Різник. – Львів : Вища школа, 1989. – 165 с.
Різник В. В. Елементи теорії впорядкованих комбінаторних наборів / В.В.Різник // Навч. посібник.- Київ: НМК ВО. – 1992.- 88 с.
Riznyk V.V. Application of Perfect Distribution Phenomenon for Acoustics and Music / V. V. Riznyk // Proc. of WSES AMT 2000, Acoustic and Music Conf., Montego Bay. – Jamaica, December 20-22, 2000. – pp. 581-585. Available at: http://www.wseas.us/e-library/conferences/jamaica2000/papers/58.pdf
Riznyk V. V. Multi-dimensional Systems Based on Perfect Combinatorial Models / V. V. Riznyk // Multidimensional Systems: Problems and Solutions. – 1998, London: IEE, Savoy Place. – pp. 5/1-5/4. doi: 10.1049/ic:19980164
Riznyk V. Application of the gold ring bundles for innovative non-redundant radar or sonar systems/ V. Riznyk, O. Bandyrska // European Physical Journal. – Special Topics. – Vol.154, Iss. 1. – 2008. – pp. 183-186. doi: 10.1140/epjst/e2008-00541-2
Riznyk V. Application of the gold ring bundles for innovative non-redundant sonar systems / V. Riznyk, O. Bandyrska, D. Skrybaylo-Leskiv // Archives of Acoustics. – Vol.31, 4(S). – 2006. – pp. 379-384. Available at: http://acoustics.ippt.gov.pl/index.php/aa/article/view/1370
Riznyk W. Application of the Golden Numerical Rings for Configure Acoustic Systems of Fine Resolution/ W. Riznyk // Acta Physica Polonica A. – 2011, Vol.119. – pp. 1046-1049. doi: 10.12693/aphyspola.119.1046
Різник В. В. Синтез дискретних сигналів з низьким рівнем автокореляційної функції бічних пелюстків за допомогою числових в’язанок / В. В. Різник, О. Я. Різник, Я. П. Кісь // Комп’ютерна інженерія та інформаційні технології. Вісник НУЛП. – 1998. – №351.- с. 132-135.
Riznyk V. Application of the perfect combinatorial configurations for configure of high performance sonar systems / V. Riznyk // Hydroacoustics Annual Journal. – 2005. – Vol.8. - Gdynia. – pp. 171-178.
Riznyk V. Nonrtdundant 2-D and 3-D sonar systems based on Gold Ring Bundles / V. Riznyk, O. Bandyrska, M. Talan // Hydroacoustics Annual Journal. – 2006. – Vol. 9. – Gdynia. – pp. 151-158.
Різник В. В. Комбінаторна оптимізація систем на основі використання спряжених симетричних та асиметричних структур / В. В. Різник // Електротехнічні та комп’ютерні системи. – 2014. – № 13(89). – с. 40-45.
Riznyk V. V. Systems Optimization Prospected from Torus Cyclic Groups / V. V. Riznyk // New Development in Pure and Applied Mathematics. – 2015. – Vienna, Austria – pp. 115-119. Available at: http://www.inase.org/library/2015/vienna/bypaper/MAPUR/MAPUR-16.pdf
Ризнык В. В. Комбинаторные конфигурации в оптимизационных задачах электросвязи / В. В. Ризнык // Электросвязь. – 1997. – №2. – с.15-17.
Різник В. В. Комбінаторні моделі та методи оптимізації в задачах інформатики / В. В. Різник // Навч. посібник. – Київ : НМК ВО. – 1991. – 72 с.
Ризнык В. В. Алгоритм построения с помощью ЭВМ полных семейств простых и многократных идеальных числовых отношений/ В. В. Ризнык, О. Я. Ризнык // Контрольно-измерительная техника. – 1985. – №38. – с.128-131.
Riznyk V. Application of the perfect combinatorial configurations for constructing non-redundant sonar or acoustic systems / V. Riznyk // 52 Open Seminar on Acoustics join with Polish-Scandinavian Structured Conference on Acoustics. – 2005, Poznan-Wagrowiec. – pp. 107-110.
Riznyk V. V. Multidimensional Systems Optimization Developed from Perfect Torus Groups / V. V. Riznyk // Int. Journal of Applied Mathematics and Informatics. – 2015. – Vol. 9. – pp. 50-54.
Riznyk V. Application of the Symmetrical and Non-symmetrical Models for Innovative Coded Design of Signals / V. Riznyk // Modern Problems of Radio Engineering Telecommunications and Computer Science TCSET’2012. – Lviv. – p. 70.
Різник В. В. Моделі оптимальних радіосистем на векторних комбінаторних конфігураціях / В. В. Різник // Вісник НТУУ «КПІ». Серія Радіотехніка, Радіоапаратобудування. – 2015. – № 60. – с. 45-58.
Різник В. В. Моделі оптимальних інформаційних систем на двовимірних комбінаторних конфігураціях / В. В. Різник // Вісник НУЛП «Інформаційні системи та мережі». – 2014. – № 805. – с. 196-204.
Різник В. В. Оптимальні коди на векторних комбінаторних конфігураціях / В.В.Різник // Вісник НУЛП «Інформаційні системи та мережі». – 2015. – № 814. – с. 130-138.
Riznyk V. Advanced Engineering Based on the Perfect Combinatorial Configurations/ V.Riznyk // Int. Journal of Engineering Technology and Advanced Engineering (IJETAE). – 2011. – Vol. 1, Issue 2. – pp. 124-126.
Питерсон У. Коды, исправляющие ошибки / У. Питерсон, Э. Уэлдон. – М. : Мир. – 1976. – 593 с.
Варакин Л. Е. Системы связи с шумоподобными сигналами / Л. Е. Варакин. – М. : Радио и связь. – 1985. – 384 с.
References
Singer J. (1938) A theorem in finite projective geometry and some applications to number theory. Transactions of the American Mathematical Society, vol. 43, no. 3, pp. 377-385.
Hall М. Jr.(1967) Combinatorial Theory. Blaisell Publishing Company, 470 p.
Riznyk V. V. and Golomb S. W. (1996) Researches and Applications of the Combinatorial Configurations for Innovative Devices and Process Engineering. CRDF Cooperative Grants Program, Los Angeles, CA 90089-2565, US, 10 p.
Riznyk V. V. (1974) Sposob dozirovaniya veshczestv [Method for measure of portions of substances. Patent USSR 429276, G 01F 11/00.
Riznyk V. V. (1975) Оb odnom sposobe optimal’nogo postroyeniya diskretnykh system [A method of the optimum design of discrete systems]. Elektronika i modelirovanie, No 8, pp.12-15.
Riznyk V. V. (1981) Ideal'nye kol'tsevye otnosheniya i vozmozhnosti ikh prakticheskogo ispol'zovaniya [An ideal circular relationship and the possibility of their practical use]. Avtomatika, No 3, pp. 87-90.
Riznyk V. V. (1989) Syntez optymalnykh kombinatornykh system [Synthesis of the combinatorial optimal systems]. Lviv, Vyshcha shkola, 165 p.
Riznyk V. V. (1992) Elementy teorii vporiadkovanykh kombinatornykh naboriv [Elements of combinatorial theory of ordered sets]. Kyiv, NMK VO Publ., 88 p.
Riznyk V. V. (2000) Application of Perfect Distribution Phenomenon for Acoustics and Music. Proc. of WSES AMT 2000, Acoustic and Music Conf., Montego Bay. Jamaica, pp. 581-585.
Riznyk V.V. (1998) Multi-dimensional Systems Based on Perfect Combinatorial Models. IEE Colloquium on Multidimensional Systems: Problems and Solutions, London, Savoy Place, P.5/1-5/4.
Riznyk V. and Bandyrska O. (2008) Application of the gold ring bundles for innovative non-redundant radar or sonar systems. The European Physical Journal. Special Topics, Vol.154, P.183- 186.
Riznyk V., Bandyrska O. and Skrybaylo-Leskiv D. (2006) Application of the gold ring bundles for innovative non-redundant sonar systems. Archives of Acoustics, Vol.31, No 4 (S), pp. 379-384.
Riznyk W. (2011) Application of the Golden Numerical Rings for Configure Acoustic Systems of Fine Resolution. Acta Physica Polonica A, Vol. 119, pp.1046 -1049.
Riznyk V. V., Riznyk O. Ya. and Kis Ya. P. (1998) Syntez dyskretnykh syhnaliv z nyzkym rivnem avtokoreliatsiinoi funktsii bichnykh peliustkiv za dopomohoiu chyslovykh v’iazanok [Synthesis of discrete signals with low side lobe autocorrelation function using numerical chains]. Visnyk NU "Lvivska politekhnika". Komp’iuterna inzheneriia ta informatsiini tekhnolohii, No 351, pp. 132-135.
Riznyk V. (2005) Application of the perfect combinatorial configurations for configure of high performance sonar systems. Hydroacoustics Annual Journal. Vol.8, pp. 171-178.
Riznyk V., Bandyrska O. and Talan M. (2006) Nonrtdundant 2-D and 3-D sonar systems based on Gold Ring Bundles. Hydroacoustics Annual Journal, Vol. 9, pp. 151-158.
Riznyk V.V. (2014) Combinatorial optimization of systems based on symmetric and asymmetric structure usage. Elektrotekhnichni ta komp'iuterni systemy, No 13(89), pp. 40-45 (in Ukrainian).
Riznyk V.V. (2015) Systems Optimization Prospected from Torus Cyclic Groups. New Development in Pure and Applied Mathematics, Vienna, Austria, March 15-17, P.115-119.
Riznyk V.V. (1997) Kombinatornye konfiguracyi v optimizacionnykh zadachakh elektrosviazi [Combinatorial configurations in optimized problems of telecommunication]. Elektrosviaz’, No 2, pp. 15-17.
Riznyk V. V. (1991) Kombinatorni modeli ta metody optymizatsii v zadachakh informatyky [Combinatorial models and optimization methods in the informatics science problems]. Kyiv, NMK VO Publ., 72 p.
Riznyk V. V. and Riznyk O. Ya. (1985) Algoritm postroeniya s pomoshch'yu EVM polnykh semeistv prostykh i mnogokratnykh ideal'nykh chislovykh otnoshenii [An algorithm for constructing complete families of simple and multiple ideal numerical relations]. Kontrol'no-izmeritel'naya tekhnika. No 38, pp. 128-131.
Riznyk V. (2005) Application of the perfect combinatorial configurations for constructing non-redundant sonar or acoustic systems. 52 Open Seminar on Acoustics join with Polish-Scandinavian Structured Conference on Acoustics, Poznan-Wagrowiec, pp. 107-110.
Riznyk V.V. (2015) Multidimensional Systems Optimization Developed from Perfect Torus Groups. International Journal of Applied Mathematics and Informatics, Vol. 9, pp. 50-54.
Riznyk V. (2012) Application of the Symmetrical and Non-symmetrical Models for Innovative Coded Design of Signals. Modern Problems of Radio Engineering Telecommunications and Computer Science (TCSET), 2012 International Conference on, p. 70.
Riznyk, V. V. (2015) Models of optimum radio-systems on the vector combinatorial configurations. Visn. NTUU KPI, Ser. Radioteh. radioaparatobuduv., no. 60, pp. 45-58. (in Ukrainian).
Riznyk V. V. (2014) Modeli optymalnykh informatsiinykh system na dvovymirnykh kombinatornykh konfihuratsiiakh [Models of optimum information systems on two-dimensional combinatorial configurations]. Visnyk NU "Lvivska politekhnika". Informatsiini systemy ta merezhi, No 805, pp. 196-204.
Riznyk V. V. (2015) Optymalni kody na vektornykh kombinatornykh konfihuratsiiakh [Optimum codes on vector combinatorial configurations]. Visnyk NU "Lvivska politekhnika". Informatsiini systemy ta merezhi, No 814, pp.130-138.
Riznyk V. (2011) Advanced Engineering Based on the Perfect Combinatorial Configurations. International Journal of Engineering Technology and Advanced Engineering, Vol. 1, Issue 2, pp.124-126.
Peterson W. W. and Weldon E. J. (1972) Error-correcting codes. MIT press.
Varakin L. E. (1985) Sistemy svyazi s shumopodobnymi signalami [Communication system with noise-like signals]. Moskow, Radio i svyaz', 384 p.
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