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Low Density Parity Check Codes Constructed from Hankel Matrices

Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, a new technique for constructing low density parity check codes based on the Hankel matrix and circulant permutation matrices is proposed. The new codes are exempt of any cycle of length 4. To ensure that parity check bits can be recursively calculated with linear computational complexity, a dual-diagonal structure is applied to the parity check matrices of those codes. The proposed codes provide a very low encoding complexity and reduce the stored memory of the matrix H in which this matrix can be easily implemented comparing to others codes used in channel coding. The new LDPC codes are compared, by simulation, with uncoded bi-phase shift keying (BPSK). The result shows that the proposed codes perform very well over additive white Gaussian noise (AWGN) channels.
Rocznik
Tom
Strony
37--41
Opis fizyczny
Bibliogr. 20 poz., rys., tab.
Twórcy
autor
  • Faculty of Electrical Engineering, Djillali Liabes University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria
autor
  • Faculty of Electrical Engineering, Djillali Liabes University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria
Bibliografia
  • [1] R. G. Gallager, „Low-density parity-check codes", IRE Transact. Inform. Theory, vol. 8, no. 1, pp. 21-28, 1962 (doi: 10.1109/TIT.1962.1057683).
  • [2] W. Sulek, „Seed Graph Expansion for Construction of Structured LDPC Codes", in Proc. 6th Int. Sym. on Wireless Commun. Sys. ISWCS, Siena, Italy, 2009, pp. 216-220 (doi: 10.1109/ISWCS.2009.5285248).
  • [3] D. Xia, H. He, Y. Xu, and Y. Cai, „A novel construction scheme with linear encoding complexity for LDPC codes", in Proc. 4th Int. Conf. on Wireless Commun. Network. and Mob. Comput., Dalian, Liaoning, China, 2008, pp. 1-4 (doi: 10.1109/WiCom.2008.358).
  • [4] R. Tanner, „A recursive approach to low complexity codes", IEEE Transact. Inform. Theory, vol. 27, no. 5, pp. 533-547, 1981 (doi: 10.1109/TIT.1981.1056404).
  • [5] Y. Abid, O. Sidek, M. F. M. Salleh, and F. Ghani, „A new quasi-cyclic low density parity check codes", in Proc. 2009 IEEE Sym. on Indust. Electron. & Applic., Kuala Lumpur, Malaysia, 2009, pp. 239-242 (doi: 10.1109/ISIEA.2009.5356472).
  • [6] D. J. C. MacKay, „Good codes based on very sparse matrices", IEEE Transact. Inform. Theory, vol. 45, no. 2, pp. 399-431, 1999 (doi: 10.1109/18.748992).
  • [7] Q. Guo-lei and Z. Dong, „Design of structured LDPC codes with quasi-cyclic and rotation architecture", in Proc. 2010 3rd Int. Conf. on Adv. Comput. Theory and Engineer. ICACTE, Chengdu, Sichuan, China, 2010, pp. 655-657 (doi: 10.1109/ICACTE.2010.5578934).
  • [8] M. Yang, W. E. Ryan, and Y. Li, „Design of efficiently encodable moderate length high-rate irregular LDPC codes", IEEE Trans. Commun., vol. 52, no. 4, pp. 564-571, 2004 (doi: 10.1109/TCOMM.2004.826367).
  • [9] K. Liu, Z. Fei, J. Kuang, and X. Li. „A novel algorithm for removing cycles in quasi-cyclic LDPC codes", in Proc. 2009 IEEE 20th Int. Sym. on Person. Indoor and Mob. Radio Commun., Tokyo, Japan, 2009, pp. 1054-1058 (doi: 10.1109/PIMRC.2009.5450003).
  • [10] A. Ahmed and Y. F. Hu, „3M Relationship Pattern for Detection and Estimation of Unknown Frequencies for Unknown Number of Sinusoids Based on Eigenspace Analysis of Hankel Matrix", in IET 2nd Intel. Sig. Process. Conf. 2013 ISP 2013, London, UK, 2013, pp. 1-6 (doi: 10.1049/cp.2013.2058).
  • [11] H. Song, J. Liu, and B. V. K. V. Kumar, „Low complexity LDPC codes for partial response channels", in Proc. IEEE Global Telecommun. Conf. GLOBECOM'02, Taipei, Taiwan, 2002, vol. 2, pp. 1294-1299 (doi: 10.1109/GLOCOM.2002.1188406).
  • [12] H. Song, J. Liu, and B. V. K. V. Kumar, „Large girth cycle codes for partial response channels", IEEE Transact. on Magnet., vol. 40, no. 4, part 2, pp. 3084-3086, 2004 (doi: 10.1109/TMAG.2004.829197).
  • [13] G. Malema and M. Liebelt, „Quasi-cyclic LDPC codes of columnweight two using a search algorithm", EURASIP J. Adv. Sig. Process., vol. 2007, no. 4, pp. 1-8, 2007 (doi: 10.1155/2007/45768).
  • [14] M. P. C. Fossorier, „Quasi-cyclic low-density parity-check codes from circulant permutation matrices", IEEE Transact. Inform. Theory, vol. 50, no. 8, pp. 1788-1793, 2004 (doi: 10.1109/TIT.2004.831841).
  • [15] M. E. O'Sulivan, „Algebraic construction of sparse matrices with large girth", IEEE Transact. Inform. Theory, vol. 52, no. 2, pp. 718-727, 2006 (doi: 10.1109/TIT.2005.862120).
  • [16] Y. Mao and A. H. Banihasherni, „A heuristic search for good low-density parity-check codes at short block lengths", in Proc. IEEE Int. Conf. on Commun. ICC'01, Helsinki, Finland, vol. 1, 2001, pp. 41-44 (doi: 10.1109/ICC.2001.936269).
  • [17] T. J. Richardson and R. L. Urbanke, „Efficient encoding of low-density-parity-check codes", IEEE Transact. Inform. Theory, vol. 47, no. 2, pp. 638-656, 2001 (doi: 10.1109/18.910579).
  • [18] L. Ping, W. K. Leung, and N. Phamdo, `Low density parity check codes with semi-random parity check matrix", Electron. Let., vol. 35, no. 1, pp. 38-39, 1999 (doi: 10.1049/el:19990065).
  • [19] Z. Hao and Z. Tong, „Block-LDPC: a partial LDPC coding system design approach", IEEE Transact. Circuits Sys. I, vol. 52, no. 4, pp. 766-775, 2005 (doi: 10.1109/TCSI.2005.844113).
  • [20] J. M. F. Moura, J. Lu, and H. Zhang, „Structured low-density-parity-check codes", IEEE Sig. Process. Mag., vol. 21, no. 1, pp. 42-55, 2004 (doi: 10.1109/MSP.2004.1267048).
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-ffaa305f-f7b3-465a-8b84-182d12f099cf
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