Skip to content


  • Research Article
  • Open Access

LDPC Code Design for Nonuniform Power-Line Channels

EURASIP Journal on Advances in Signal Processing20072007:076146

  • Received: 28 October 2006
  • Accepted: 1 May 2007
  • Published:


We investigate low-density parity-check code design for discrete multitone channels over power lines. Discrete multitone channels are well modeled as nonuniform channels, that is, different bits experience various channel parameters. We propose a coding system for discrete multitone channels that allows for using a single code over a nonuniform channel. The number of code parameters for the proposed system is much greater than the number of code parameters in conventional channel. Therefore, search-based optimization methods are impractical. We first formulate the problem of optimizing the rate of an irregular low-density parity-check code, with guaranteed convergence over a general nonuniform channel, as an iterative linear programming which is significantly more efficient than search-based methods. Then we use this technique for a typical power-line channel. The methodology of this paper is directly applicable to all decoding algorithms for which a density evolution analysis is possible.


  • Power Line
  • Code Design
  • LDPC Code
  • Channel Parameter
  • Density Evolution


Authors’ Affiliations

Department of Electrical and Computer Engineering, Faculty of Engineering, University of Alberta, Edmonton, AB, T6G 2V4, Canada


  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. Pishro-Nik H, Rahnavard N, Fekri F: Nonuniform error correction using low-density parity-check codes. IEEE Transactions on Information Theory 2005,51(7):2702-2714. 10.1109/TIT.2005.850230MathSciNetView ArticleMATHGoogle Scholar
  7. 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 ArticleMATHGoogle Scholar
  8. Roumy A, Guemghar S, Caire G, Verdú S: Design methods for irregular repeat-accumulate codes. IEEE Transactions on Information Theory 2004,50(8):1711-1727. 10.1109/TIT.2004.831778View ArticleMathSciNetMATHGoogle Scholar
  9. Ardakani M, Kschischang FR: A more accurate one-dimensional analysis and design of irregular LDPC codes. IEEE Transactions on Communications 2004,52(12):2106-2114. 10.1109/TCOMM.2004.838718View ArticleGoogle Scholar
  10. Gallager RG: Low-Density Parity-Check Codes. The MIT Press, Cambridge, Mass, USA; 1963.MATHGoogle Scholar
  11. Shokrollahi A: New sequence of linear time erasure codes approaching the channel capacity. Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC '99), November 1999, Honolulu, Hawaii, USA, Lecture Notes in Computer Science 1719: 65-67.MathSciNetMATHGoogle Scholar
  12. 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
  13. Luby MG, Mitzenmacher M, Shokrollahi MA, Spielman DA: Improved low-density parity-check codes using irregular graphs. IEEE Transactions on Information Theory 2001,47(2):585-598. 10.1109/18.910576MathSciNetView ArticleMATHGoogle Scholar
  14. Tanner RM: A recursive approach to low complexity codes. IEEE Transactions on Information Theory 1981,27(5):533-547. 10.1109/TIT.1981.1056404MathSciNetView ArticleMATHGoogle Scholar
  15. 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 ArticleMATHGoogle Scholar
  16. 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 ArticleMATHGoogle Scholar
  17. ten Brink S, Kramer G, Ashikhmin A: Design of low-density parity-check codes for modulation and detection. IEEE Transactions on Communications 2004,52(4):670-678. 10.1109/TCOMM.2004.826370View ArticleGoogle Scholar
  18. Mannoni V, Declereq D, Gelle G: Optimized irregular Gallager codes for OFDM transmission. Proceedings of the 13th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications Conference (PIMRC '02), September 2002, Lisboa, Portugal 1: 222-226.View ArticleGoogle Scholar
  19. de Baynast A, Sabharwal A, Aazhang B: LDPC code design for OFDM channel: graph connectivity and information bits positioning. Proceedings of International Symposium on Signals, Circuits and Systems (ISSCS '05), July 2005, Iasi, Romania 2: 649-652.Google Scholar
  20. 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 ArticleMATHGoogle 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 ArticleMATHGoogle Scholar
  22. Ungerboeck G: Channel coding with multilevel/phase signals. IEEE Transactions on Information Theory 1982,28(1):55-67. 10.1109/TIT.1982.1056454MathSciNetView ArticleMATHGoogle Scholar
  23. Caire G, Taricco G, Biglieri E: Bit-interleaved coded modulation. IEEE Transactions on Information Theory 1998,44(3):927-946. 10.1109/18.669123MathSciNetView ArticleMATHGoogle Scholar
  24. Hou J, Siegel PH, Milstein LB, Pfister HD: Capacity-approaching bandwidth-efficient coded modulation schemes based on low-density parity-check codes. IEEE Transactions on Information Theory 2003,49(9):2141-2155. 10.1109/TIT.2003.815777MathSciNetView ArticleMATHGoogle Scholar
  25. Chung S-Y, Richardson TJ, Urbanke RL: Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation. IEEE Transactions on Information Theory 2001,47(2):657-670. 10.1109/18.910580MathSciNetView ArticleMATHGoogle Scholar
  26. Ardakani M, Smith B, Yu W, Kschischang F: Complexity-optimized low-density parity-check codes. In Proceedings of the 43rd Annual Allerton Conference on Communication, Control, and Computing, September 2005, Monticello, Ill, USA. Allerton House;Google Scholar
  27. Esmailian T, Kschischang FR, Gulak PG: In-building power lines as high-speed communication channels: channel characterization and a test channel ensemble. International Journal of Communication Systems 2003,16(5):381-400. 10.1002/dac.596View ArticleGoogle Scholar