Skip to content


  • Research Article
  • Open Access

Near-Capacity Coding for Discrete Multitone Systems with Impulse Noise

  • 1,
  • 2 and
  • 2
EURASIP Journal on Advances in Signal Processing20062006:098738

  • Received: 1 December 2004
  • Accepted: 9 June 2005
  • Published:


We consider the design of near-capacity-achieving error-correcting codes for a discrete multitone (DMT) system in the presence of both additive white Gaussian noise and impulse noise. Impulse noise is one of the main channel impairments for digital subscriber lines (DSL). One way to combat impulse noise is to detect the presence of the impulses and to declare an erasure when an impulse occurs. In this paper, we propose a coding system based on low-density parity-check (LDPC) codes and bit-interleaved coded modulation that is capable of taking advantage of the knowledge of erasures. We show that by carefully choosing the degree distribution of an irregular LDPC code, both the additive noise and the erasures can be handled by a single code, thus eliminating the need for an outer code. Such a system can perform close to the capacity of the channel and for the same redundancy is significantly more immune to the impulse noise than existing methods based on an outer Reed-Solomon (RS) code. The proposed method has a lower implementation complexity than the concatenated coding approach.


  • Gaussian Noise
  • Main Channel
  • White Gaussian Noise
  • Degree Distribution
  • Additive Noise

Authors’ Affiliations

Department of Electrical and Computer Engineering, University of Alberta, ECERF Building, Edmonton, AB, T6G 2V4, Canada
Department of Electrica and Computer Engineering, University of Toronto, 10 King's College Road, Toronto, ON, M5S 3G4, Canada


  1. Zogakis TN, Aslanis JT Jr., Cioffi JM: Analysis of a concatenated coding scheme for a discrete multitone modulation system. Proceedings of IEEE Military Communications Conference (MILCOM '94), October 1994, Fort Monmouth, NJ, USA 2: 433–437.Google Scholar
  2. Zhang L, Yongacoglu A: Turbo coding in ADSL DMT systems. Proceedings of IEEE International Conference on Communications (ICC '01), June 2001, Helsinki, Finland 1: 151–155.Google Scholar
  3. Cai Z, Subramanian KR, Zhang L: DMT scheme with multidimensional turbo trellis code. Electronics Letters 2000, 36(4):334–335. 10.1049/el:20000259View ArticleGoogle Scholar
  4. Ardakani M, Esmailian T, Kschischang FR: Near-capacity coding in multicarrier modulation systems. IEEE Transactions on Communications 2004, 52(11):1880–1889. 10.1109/TCOMM.2004.836560View ArticleGoogle Scholar
  5. Eleftheriou E, Ölçer S: Low-density parity-check codes for digital subscriber lines. Proceedings of IEEE International Conference on Communications (ICC '02), April—May 2002, New York, NY, USA 3: 1752–1757.View ArticleGoogle Scholar
  6. Cooklev T, Tzannes M, Friedman A: Low-density parity-check coded modulation for ADSL. In Temporary Document BI-081. ITU-Telecommunication Standardization Sector, Geneva, Switzerland; October 2000.Google Scholar
  7. Berrou C, Glavieux A, Thitimajshima P: Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1. Proceedings of IEEE International Conference on Communications (ICC '93), May 1993, Geneva, Switzerland 2: 1064–1070.View ArticleGoogle Scholar
  8. Divsalar D, Pollara F: On the design of turbo codes. In TDA Progr. Rep. 42–123. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, Calif, USA; 1995.Google Scholar
  9. Richardson TJ, Urbanke RL: The capacity of low-density parity-check codes under message-passing decoding. IEEE Transactions on Information Theory 2001, 47(2):599–618. 10.1109/18.910577MathSciNetView ArticleGoogle Scholar
  10. Richardson TJ, Shokrollahi MA, Urbanke RL: Design of capacity-approaching irregular low-density parity-check codes. IEEE Transactions on Information Theory 2001, 47(2):619–637. 10.1109/18.910578MathSciNetView ArticleGoogle Scholar
  11. Shokrollahi A: Capacity-achieving sequences. In Codes, Systems, and Graphical Models, IMA Volumes in Mathematics and Its Applications. Edited by: Marcus B, Rosenthal J. Springer, New York, NY, USA; 2000:153–166.Google Scholar
  12. Imai H, Hirakawa S: A new multilevel coding method using error-correcting codes. IEEE Transactions on Information Theory 1977, 23(3):371–377. 10.1109/TIT.1977.1055718View ArticleGoogle Scholar
  13. Caire G, Taricco G, Biglieri E: Bit-interleaved coded modulation. IEEE Transactions on Information Theory 1998, 44(3):927–946. 10.1109/18.669123MathSciNetView ArticleGoogle Scholar
  14. Forney GD Jr., Ungerboeck G: Modulation and coding for linear Gaussian channels. IEEE Transactions on Information Theory 1998, 44(6):2384–2415. 10.1109/18.720542MathSciNetView ArticleGoogle Scholar
  15. Yu W, Toumpakaris D, Cioffi JM, Gardan D, Gauthier F: Performance of asymmetric digital subscriber lines in an impulse noise environment. IEEE Transactions on Communications 2003, 51(10):1653–1657. 10.1109/TCOMM.2003.818107View ArticleGoogle Scholar
  16. Barton M: Impulse noise performance of an asymmetric digital subscriber lines passband transmission system. IEEE Transactions on Communications 1995, 43(234):1337–1340.View ArticleGoogle Scholar
  17. Kerpez KJ, Gottlieb AM: The error performance of digital subscriber lines in the presence of impulse noise. IEEE Transactions on Communications 1995, 43(5):1902–1905. 10.1109/26.387412View ArticleGoogle Scholar
  18. Toumpakaris D, Yu W, Cioffi JM, Gardan D, Ouzzif M: A byte-erasure method for improved impulse immunity in DSL systems using soft information from an inner code. Proceedings of IEEE International Conference on Communications (ICC '03), May 2003, Anchorage, Alaska, USA 4: 2431–2435.View ArticleGoogle Scholar
  19. Toumpakaris D, Cioffi JM, Gardan D, Ouzzif M: A square distance-based byte-erasure method for reduced-delay protection of DSL systems from non-stationary interference. Proceedings of IEEE Global Telecommunications Conference (GLOBECOM '03), December 2003, San Francisco, Calif, USA 4: 2114–2119.View ArticleGoogle Scholar
  20. Chow PS: Bandwidth optimized digital transmission techniques for spectrally shaped channels with impulse noise, M.S. thesis. Department of Electrical Engineering, Stanford University, Stanford, Calif, USA; May 1993.Google Scholar
  21. Wachsmann U, Fischer RFH, Huber JB: Multilevel codes: theoretical concepts and practical design rules. IEEE Transactions on Information Theory 1999, 45(5):1361–1391. 10.1109/18.771140MathSciNetView ArticleGoogle Scholar
  22. Pottie GJ, Taylor DP: Multilevel codes based on partitioning. IEEE Transactions on Information Theory 1989, 35(1):87–98. 10.1109/18.42180MathSciNetView ArticleGoogle Scholar
  23. Calderbank AR: Multilevel codes and multistage decoding. IEEE Transactions on Communications 1989, 37(3):222–229. 10.1109/26.20095MathSciNetView ArticleGoogle Scholar
  24. Tanner RM: A recursive approach to low complexity codes. IEEE Transactions on Information Theory 1981, 27(5):533–547. 10.1109/TIT.1981.1056404MathSciNetView ArticleGoogle Scholar
  25. Kschischang FR, Frey BJ, Loeliger H-A: Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory 2001, 47(2):498–519. 10.1109/18.910572MathSciNetView ArticleGoogle Scholar
  26. Luby MG, Mitzenmacher M, Shokrollahi MA, Spielman DA: Efficient erasure correcting codes. IEEE Transactions on Information Theory 2001, 47(2):569–584. 10.1109/18.910575MathSciNetView ArticleGoogle Scholar
  27. Chung S-Y, Forney GD Jr., Richardson TJ, Urbanke R: On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit. IEEE Communications Letters 2001, 5(2):58–60. 10.1109/4234.905935View ArticleGoogle Scholar
  28. Hou J, Siegel PH, Milstein LB, Pfister D: Multilevel coding with low-density parity-check component codes. Proceedings of IEEE Global Telecommunications Conference (GLOBECOM '01), November 2001, San Antonio, Tex, USA 2: 1016–1020.View ArticleGoogle Scholar
  29. Ungerboeck G: Channel coding with multilevel/phase signals. IEEE Transactions on Information Theory 1982, 28(1):55–67. 10.1109/TIT.1982.1056454MathSciNetView ArticleGoogle Scholar
  30. Ardakani M, Chan TH, Kschischang FR: EXIT-chart properties of the highest-rate LDPC code with desired convergence behavior. IEEE Communications Letters 2005, 9(1):52–54. 10.1109/LCOMM.2005.1375239View ArticleGoogle Scholar
  31. ten Brink S: Convergence behavior of iteratively decoded parallel concatenated codes. IEEE Transactions on Communications 2001, 49(10):1727–1737. 10.1109/26.957394View ArticleGoogle Scholar
  33. Hou J, Siegel PH, Milstein LB: Performance analysis and code optimization of low density parity-check codes on Rayleigh fading channels. IEEE Journal on Selected areas in Communications 2001, 19(5):924–934. 10.1109/49.924876View ArticleGoogle Scholar
  34. Flarion Inc., "Vector-LDPC Coding Solution Data Sheet",
  35. Tian T, Jones C, Villasenor JD, Wesel RD: Construction of irregular LDPC codes with low error floors. Proceedings of IEEE International Conference on Communications (ICC '03), May 2003, Anchorage, Alaska, USA 5: 3125–3129.View ArticleGoogle Scholar


© Ardakani et al. 2006