Extrinsic information transfer functions: Model and erasure channel properties

IEEE Transactions on Information Theory

Volumn 50, Issue 11, 2004, Pages 2657-2673

  Ashikhmin, Alexei ^a   Kramer, Gerhard ^a   ten Brink, Stephan ^b  

^a LUCENT TECHNOLOGIES   (United States)

^b Realtek Semiconductors   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CURVE FITTING; DECODING; ERROR CORRECTION; ITERATIVE METHODS; MATHEMATICAL MODELS; THEOREM PROVING; TURBO CODES;

CONCATENATED CODES; ERROR CORRECTION CODING; EXTRINSIC INFORMATION TRANSFER FUNCTIONS; ITERATIVE DECODING; LOW DENSITY PARITY CHECK CODES; MUTUAL INFORMATION;

COMMUNICATION CHANNELS (INFORMATION THEORY);

EID: 2442425417     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2004.836693     Document Type: Article

References (60)

1. R. G. Gallager, Low-Density Parity-Check Codes. Cambridge, MA: MIT Press, 1963.
2. M. G. Luby, M. Mitzenmacher, M. A. Shokrollahi, D. A. Spielman, and V. Stemann, "Practical loss-resilient codes," in Proc. 29th Annu. ACM Symp. Theory of Computing, 1997, pp. 150-159.
3. M. G. Luby, M. Mitzenmacher, M. A. Shokrollahi, and D. A. Spielman, "Efficient erasure correcting codes," IEEE Trans. Inform. Theory, vol. 47, pp. 569-584, Feb. 2001.
4. T. J. Richardson and R. L. Urbanke, "The capacity of low-density parity-check codes under message-passing decoding," IEEE Trans. Inform. Theory, vol. 47, pp. 599-618, Feb. 2001.
5. T. J. Richardson, A. Shokrollahi, and R. L. Urbanke, "Design of capacity-approaching low-density parity-check codes," IEEE Trans. Inform. Theory, vol 47, pp. 619-637, Feb. 2001.
6. S. Y. Chung, "On the construction of some capacity-approaching coding schemes," Ph,D. dissertation, MIT, Cambridge, MA, 2000.
7. S. ten Brink, "Convergence of iterative decoding," Electron. Lett., vol. 35, no. 10, pp. 806-808, May 1999.
8. D. Divsalar, S. Dolinar, and F. Pollara, "Low complexity turbo-like codes," in Proc. 2nd Int. Symp. Turbo Codes, Sept. 2000, pp. 73-80.
9. S. ten Brink, "Designing iterative decoding schemes with the extrinsic information transfer chart," AEÜ Int. J. Electron. Commun., vol. 54, no. 6, pp. 389-398, Dec. 2000.
10. S. Y. Chung, T. J. Richardson, and R. Urbanke, "Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation," IEEE Trans. Inform. Theory, vol. 47, pp. 657-670, Feb. 2001.
11. H. El Gamal and A. R. Hammons Jr, "Analyzing the turbo decoder using the Gaussian approximation," IEEE Trans. Inform. Theory, vol. 47, pp. 671-686, Feb. 2001.
12. K. Narayanan, "Effect of precoding on the convergence of turbo equalization for partial response channels," IEEE J. Select. Areas Commun., vol. 19, pp. 686-698, Apr. 2001.
13. S. ten Brink, "Convergence behavior of iteratively decoded parallel concatenated codes," IEEE Trans. Commun., vol. 49, pp. 1727-1737, Oct. 2001.
14. S. Huettinger, J. Huber, R. Johannesson, and R. Fischer, " Information processing in soft-output decoding," in Proc. Allerton Conf. Communication, Control, and Computing, Allerton, IL, Oct. 2001.
15. J. Boutros and G. Caire, "Iterative multiuser joint decoding: Unified framework and asymptotic analysis," IEEE Trans. Inform. Theory, vol. 48, pp. 1772-1793, July 2002.
16. J. Huber and S. Huettinger, "Information processing and combining in channel coding," in Proc. 3rd Int. Symp. Turbo Codes, Brest, France, Sept. 1-5, 2003, pp. 95-102.
17. F. Lehmann and G. M. Maggio, "Analysis of the iterative decoding of LDPC and product codes using the Gaussian approximation," IEEE Trans. Inform. Theory, vol. 49, pp. 2993-3000, Nov. 2003.
18. M. Tüchler, S. ten Brink, and J. Hagenauer, "Measures for tracing convergence of iterative decoding algorithms," in Proc. 4th Int. ITG Conf. Source and Channel Coding, Berlin, Germany, Jan. 2002.
19. B. Scanavino, G. Montorsi, and S. Benedetto, "Convergence properties of iterative decoders working at bit and symbol level," in Proc. 2001 IEEE Global Telecommunications Conf. (GLOBECOM '01), vol. 2, 2001, pp. 1037-1041.
20. C. Berrou and A. Glavieux, "Near optimum error correcting coding and decoding: Turbo-codes," IEEE Trans. Commun., vol. 44, pp. 1261-1271, Oct. 1996.
21. S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara, "Serial concatenation of interleaved codes: Performance analysis, design, and iterative decoding," IEEE Trans. Inform. Theory, vol. 44, pp. 909-926, May 1998.
22. D. Divsalar, H. Jin, and R. J. McEliece, "Coding theorems for 'turbo-like' codes," in Proc. Allerton Conf. Communication, Control, and Computing, Allerton, IL, Sept. 1998, pp. 201-210.
23. H. Jin, A. Khandekar, and R. McEliece, "Irregular repeat-accumulate codes," in Proc. 2nd Int. Conf. Turbo Codes, Brest, France, Sept. 2000.
24. S. ten Brink, "Rate one-half code for approaching the Shannon limit by 0.1 dB," Electron. Lett., vol. 36, no. 15, pp. 1293-1294, July 2000.
25. D. Divsalar, S. Dolinar, and F. Pollara, "Iterative turbo decoder analysis based on density evolution," IEEE J. Select. Areas Commun., vol. 19, pp. 891-907, May 2001.
26. M. Tüchler and J. Hagenauer, "EXIT charts of irregular codes," in Proc. 36th Annu. Conf. Information Science and Systems, Princeton, NJ, Mar. 2002.
27. G. Caire, D. Burshtein, and S. Shamai (Shitz), "LDPC coding for interference mitigation at the transmitter," in Proc. Allerton Conf. Communication, Control, and Computing, Allerton, IL, Oct. 2002.
28. S. ten Brink and G. Kramer, "Design of repeat-accumulate codes for iterative detection and decoding," IEEE Trans. Signal Processing, vol. 51, pp. 2764-2772, Nov. 2003.
29. M. Tüchler, "Design of serially concatenated systems depending on the block length," IEEE Trans. Commun., vol. 52, pp. 209-218, Feb. 2004.
30. S. ten Brink, G. Kramer, and A. Ashikhmin, "Design of low-density parity-check codes for modulation and detection," IEEE Trans. Commun., vol. 52, pp. 670-678, Apr. 2004.
31. M. A. Shokrollahi, "Capacity-achieving sequences," in Codes, Systems, and Graphical Models, B. Marcus and J. Rosenthal, Eds. Minneapolis, MN: Inst. Math. and its Applic., Univ. Minnesota, 2000, vol. 123, IMA Volumes in Mathematics and its Applications, pp. 153-166.
32. T. Helleseth, T. Kløve, and V. I. Levenshtein, "On the information function of an error-correcting code," IEEE Trans. Inform. Theory, vol. 43, pp. 549-557, Mar. 1997.
33. V. K. Wei, "Generalized Hamming weights for linear codes," IEEE Trans. Inform. Theory, vol. 37, pp. 1412-1418, Sept. 1991.
34. T. Kløve, "Support weight distribution for linear codes," Discr. Math., vol. 106/107, pp. 311-316, 1992.
35. J. Simonis, "The effective length of subcodes," Applicable Algebra in Eng., Commun., and Comput., vol. 5, pp. 371-377, 1994.
36. J. Hagenauer, E. Offer, and L. Papke, "Iterative decoding of binary block and convolutional codes," IEEE Trans. Inform. Theory, vol. 42, pp. 429-445, Mar. 1996.
37. R. G. Gallager, Information Theory and Reliable Communication. New York: Wiley, 1968.
38. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley, 1991.
39. I. Land, P. A. Hoeher, S. Huettinger, and J. Huber, "Bounds on information combining," in Proc. 3rd Int. Symp. Turbo Codes, Brest, France, Sept. 1-5, 2003, pp. 39-42.
40. I. Sutskover, S. Shamai (Shitz), and J. Ziv, "Extremes of information combining," in Proc. Allerton Conf. Communication, Control, and Computing, Allerton, IL, Oct. 2003.
41. S. ten Brink, "Exploiting the chain rule of mutual information for the design of iterative decoding schemes," in Proc. Allerton Conf. Communication, Control, and Computing, Allerton, IL, Oct. 2001.
42. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes.. Amsterdam, The Netherlands: North-Holland, 1977.
43. l - 1)/N)," Discr. Math., vol. 18, pp. 179-211, 1977.
44. C. Bachoc, "On harmonic weight enumerators of binary codes," Des., Codes, Cryptogr., vol. 18, pp. 11-28, 1999.
45. H. Chen and J. Coffey, "Trellis structure and higher weights of extremal self-dual codes," Des., Codes, Cryptogr., vol. 24, pp. 15-36, 2001.
46. S. Dougherty, A. Gulliver, and M. Oura, "Higher weights and graded rings for binary self-dual codes," unpublished paper, submitted for publication.
47. O. Milenkovic, "Higher weight and coset weight enumerators of formally self-dual codes," Des., Codes, Cryptogr., to be published.
48. O. Milenkovic, S. T. Coffey, and K. J. Compton, "The third support weight enumerators of the doubly-even, self-dual [32, 16, 8] codes," IEEE Trans. Inform. Theory, vol. 49, pp. 740-746, Mar. 2003.
49. S. Benedetto and G. Montorsi, "Unveiling turbo codes: Some results on parallel concatenated coding schemes," IEEE Trans. Inform. Theory, vol. 42, pp. 409-428, Mar. 1996.
50. C. Di, D. Proietti, I. E. Telatar, T. J. Richardson, and R. L. Urbanke, "Finite-length analysis of low-density parity-check codes on the binary erasure channel," IEEE Trans. Inform. Theory, vol. 48, pp. 1570-1579, June 2002.
51. C. E. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J., vol. 27, pp. 379-423, July 1948.
52. S. ten Brink, "Code doping for triggering iterative decoding convergence," in Proc. 2001 IEEE Int. Symp. Information Theory, Washington, DC, June 2001, p. 235.
53. M. A. Shokrollahi, "New sequences of linear time erasure codes approaching the channel capacity," in Proc. 13th Conf. Applied Algebra, Error Correcting Codes, and Cryptography (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 1999, pp. 65-76.
54. P. Oswald and A. Shokrollahi, "Capacity-achieving sequences for the erasure channel," IEEE Trans. Inform. Theory, vol. 48, pp. 3017-3028, Dec. 2002.
55. M. Lentmaier and K. S. Zigangirov, "On generalized low-density parity-check codes based on Hamming component codes," IEEE Commun. Lett., vol. 3, pp. 248-250, Aug. 1999.
56. A. Ashikhmin and S. Litsyn, "Fast MAP decoding of first order Reed-Muller and Hamming codes," IEEE Trans. Inform. Theory, submitted for publication.
57. S. Huettinger, S. ten Brink, and J. Huber, "Turbo-code representation of RA-codes and DRS-codes for reduced complexity decoding," in Proc. 2001 Conf. Information Science and Systems, Mar. 21-23, 2001.
58. I. N. Bronshtein and K. A. Semendyayev, Handbook of Mathematics, 3rd ed. Berlin, Germany: Springer-Verlag, 1997.
59. F. J. MacWilliams, "A theorem on the distribution of weights in a systematic code," Bell Syst. Tech. J., vol. 42, pp. 79-94, 1963.
60. E. Sharon, A. Ashikhmin, and S. Litsyn, "EXIT functions for the Gaussian channel," in Proc. Allerton Conf. Communication, Control, and Computing, Monticello, IL, Oct. 2003, pp. 972-981.