Recent advances in turbo code design and theory

Proceedings of the IEEE

Volumn 95, Issue 6, 2007, Pages 1323-1344

  Vucetic, Branka ^a   Li, Yonghui ^a   Perez, Lance C ^b   Jiang, Fan ^b,c  

^a UNIVERSITY OF SYDNEY   (Australia)

^b UNIVERSITY OF NEBRASKA LINCOLN   (United States)

^c TUSKEGEE UNIVERSITY   (United States)

Author keywords

Interleavers; Iterative decoding; Low density parity check (LDPC) codes; Turbo codes

Indexed keywords

CHANNEL CODING; FORWARD ERROR CORRECTION; ITERATIVE DECODING; MATRIX ALGEBRA;

CODE DESIGNS; DESIGN AND THEORIES; EXPLICIT FORMULATION; INTERLEAVER DESIGN; INTERLEAVERS; LOW-DENSITY PARITY-CHECK (LDPC) CODES; PARITY CHECK MATRICES; SUM-PRODUCT DECODING;

TURBO CODES;

EID: 57849132921     PISSN: 00189219     EISSN: None     Source Type: Journal    
DOI: 10.1109/JPROC.2007.897975     Document Type: Article

References (73)

1. C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon limit error-correcting coding and decoding: Turbo-codes," in Proc. 1993 IEEE Int. Conf. Communications, pp. 1064-1070.
2. C. Berrou and A. Glavieux, "Near optimum error correcting coding and decoding: Turbo-codes," IEEE Trans. Commun., vol. 44, no. 10, pp. 1261-1271, Oct. 1996.
3. R. G. Gallager, Low-Density Parity-Check Codes. Cambridge, MA: MIT Press, 1963.
4. D. J. C. MacKay and R. M. Neal, "Near Shannon limit performance of low density parity check codes," IEE Electron. Lett., vol. 32, no. 18, pp. 1645-1646, Aug. 1996.
5. S. Benedetto and G. Montorsi, "Unveiling turbo codes: Some results on parallel concatenated coding schemes," IEEE Trans. Inf. Theory, vol. 42, no. 2, pp. 409-428, Mar. 1996.
6. L. C. Pérez, J. Seghers, and D. J. Costello, Jr., "A distance spectrum interpretation of turbo codes," IEEE Trans. Inf. Theory, vol. 42, no. 6, pp. 1698-1709, Nov. 1996.
7. S. Benedetto and G. Montorsi, "Design of parallel concatenated convolutional codes," IEEE Trans. Commun., vol. 44, no. 5, pp. 591-600, May 1996.
8. S. ten Brink, "Convergence behavior of iterative decoded parallel concatenated codes," IEEE Trans. Commun., vol. 49, no. 10, pp. 1727-1737, Oct. 2001.
9. S. ten Brink, "Designing iterative decoding schemes with the extrinsic information transfer chart," AEU Int. J. Electron. Commun., vol. 54, pp. 389-398, Nov. 2000.
10. O. Takeshita, O. Collins, P. Massey, and D. J. Costello, Jr., "A note on asymmetric turbo codes," IEEE Commun. Letters, vol. 3, no. 3, pp. 69-71, Mar. 1999.
11. P.Massey, O. Takeshita, and D. J. Costello, Jr., "Contradicting a myth: Good turbo codes with large memory order," in Proc. Int. Symp. Information Theory, 2000, p. 122.
12. F. Jiang, M. Becker, and L. C. Pérez, "Time-varying turbo codes," IEEE Commun. Letters, vol. 8, no. 8, pp. 529-531, Aug. 2004.
13. J. G. Proakis, Digital Communications, 3rd ed. New York: McGraw-Hill, 1995.
14. C. B. Schlegel and L. C. Pérez, Trellis and Turbo Coding. New York: IEEE Press/Wiley, 2003.
15. B. Vucetic and J. Yuan, Turbo Codes Principles and Applications. Boston, MA: Kluwer, 2000.
16. S. Benedetto, G. Montorsi, and D. Divsalar, "Concatenated convolutional codes with interleavers," IEEE Commun. Mag., vol. 41, no. 8, pp. 102-109, Aug. 2003.
17. J. Yuan, B. Vucetic, and W. Feng, "Combined turbo codes and interleaver design," IEEE Trans. Commun., vol. 47, no. 4, pp. 484-487, Apr. 1999.
18. F. Daneshgaran and M. Laddomada, "Optimized prunable single-cycle interleavers for turbo codes," IEEE Trans. Commun., vol. 52, no. 6, pp. 899-909, Jun. 2004.
19. S. Dolinar and D. Divsalar, "Weight distribution for turbo codes using random and nonrandom permutations," JPL, TDA Progress Rep. 42-122, Aug. 1995, pp. 56-65.
20. A. S. Barbulescu and S. S. Pietrobon, "Terminating the trellis of turbo-codes in the same state," Electron. Lett., vol. 31, no. 1, pp. 22-23, Jan. 1995.
21. J. Ramsey, "Realization of optimum interleavers," IEEE Trans. Inf. Theory, vol. 16, no. 3, pp. 338-345, May 1970.
22. G. Forney, Jr., "Burst-correcting codes for the classic bursty channel," IEEE Trans. Commun., vol. 19, no. 5, pp. 772-781, Oct. 1971.
23. E. K. Hall and S. G. Wilson, "Stream-oriented turbo codes," IEEE Trans. Inf. Theory, vol. 47, no. 5, pp. 1813-1831, Jul. 2001.
24. E. K. Hall and S. G. Wilson, "Stream-oriented parallel concatenated convolutional codes," in Proc. IEEE Information Theory Workshop, 1998, pp. 4-5.
25. J. Yuan et al., "Design of cyclic shift interleavers for turbo codes," Ann. Telecommun., vol. 56, no. 7-8, pp. 384-393, Jul.-Aug. 2001.
26. F. Daneshgaran and M. Mondin, "Design of interleavers for turbo codes: Iterative interleaver growth algorithms of polynomial complexity," IEEE Trans. Inf. Theory, vol. 45, no. 6, pp. 1845-1859, Sep. 1999.
27. F. Daneshgaran and M. Mondin, "Optimized turbo codes for delay constrained applications," IEEE Trans. Inf. Theory, vol. 48, no. 1, pp. 293-305, Jan. 2002.
28. W. Feng, J. Yuan, and B. Vucetic, "A code matched interleaver design for turbo codes," IEEE Trans. Commun., vol. 50, no. 6, pp. 926-937, Jun. 2002.
29. D. L. Ruyet, S. Hong, and H. V. Thien, "An interleaver design algorithm based on a cost matrix for turbo codes," in Proc. 2000 Int. Symp. Information Theory, p. 452.
30. P. Robertson, "Improving decoder and code structure of parallel concatenated recursive systematic (turbo) codes," in IEEE Int. Conf. Universal Personal Communications, Oct. 1994, pp. 183-187.
31. J. Hokfelt and T. Maseng, "Methodical interleaver design for turbo codes," in Proc. Int. Symp. Turbo Codes and Related Topics, 1997, pp. 212-215.
32. A. Abbasfar and K. Yao, "Interleaver design for turbo codes by distance spectrum shaping," in Proc. WCNC'04, vol. 3, pp. 1616-1619.
33. J. Hokfelt, O. Edfors, and T. Maseng, "On the theory and performance of trellis termination methods for turbo codes," IEEE J. Sel. Areas Commun., vol. 19, no. 5, pp. 838-847, May 2001.
34. N. Ehtiati, A. Ghrayeb, and M. R. Soleymani, "Improved interleaver design for turbo coded intersymbol interference channels," in Proc. 2003 Vehicular Technology Conf. (VTC 2003VFall), vol. 1, pp. 327-331.
35. F. Daneshgaran and M. Laddomada, "An improved interleaver design technique for parallel concatenated convolutional codes," in Proc. 2003 Int. Conf. Communications, vol. 5, pp. 3100-3104.
36. C. Schlegel and L. Perez, "On error bounds and turbo-codes," IEEE Commun. Lett., vol. 3, no. 7, pp. 205-207, Jul. 1999.
37. N. Ehtiati, M. R. Soleymani, and H. Sadjadpour, "Joint interleaver design for multiple turbo codes," in Proc. VTC2004VFall 2004, vol. 4, pp. 2302-2306.
38. M. Z. Wang, A. Sheikh, and F. Qi, "Interleaver design for short turbo codes," in Proc. Globecom'99, vol. 1B, pp. 894-898.
39. J. Garcia-Frias and F. Cabarcas, "Reducing the error floor in turbo codes by using non-binary constituent encoders," in Proc. IEEE VTC 2000-Fall, vol. 3, pp. 1230-1237.
40. S. Crozier and P. Guinand, "High-performance low-memory interleaver banks for turbo-codes," in Proc. VTC'2001VFall, vol. 4, pp. 2394-2398.
41. D. Truhachev, D. Lentmaier, O. Wintzell, and K. Zingangirov, "On the minimum distance of turbo codes," in Proc. 2002 IEEE Int. Symp. Information Theory, p. 84.
42. X. Zhang, D. Yuan, and J. Luo, "Code-matched interleaver for turbo codes," in Proc. WCNC'04, vol. 3, pp. 1607-1610.
43. K. Wu, H. Li, and Y. Wang, "Influence of interleaver on minimum turbo code distance," Electron. Lett., vol. 35, no. 17, pp. 1456-1458, Aug. 1999.
44. M. Z. Wang, A. Sheikh, and F. Qi, "Interleaver design for short turbo codes," in Proc. IEEE Globecom, 1999, vol. 1B, pp. 894-898.
45. J. Hokfelt, O. Edforts, and T. Maseng, "A turbo code interleaver design criterion based on the performance of iterative decoding," IEEE Commun. Lett., vol. 5, no. 2, pp. 52-54, Feb. 2001.
46. J. Hokfelt, O. Edfors, and T. Maseng, "Turbo codes: Correlated extrinsic information and its impact on iterative decoding performance," in Proc. VTC'99, vol. 3, pp. 1871-1875.
47. J. Hokfelt, O. Edfors, and T. Maseng, "Interleaver design for turbo codes based on the performance of iterative decoding," in Proc. ICC'99, vol. 1, pp. 93-97.
48. S. Benedetto and G. Montorsi, "Performance of continuous and blockwise decoded turbo codes," IEEE Commun. Lett., vol. 1, no. 3, pp. 77-79, May 1997.
49. H. R. Sadjadpour, N. J. A. Sloane, M. Salehi, and G. Nebe, "Interleaver design for turbo codes," IEEE J. Sel. Areas Commun., vol. 19, no. 5, pp. 831-837, Nov. 2001.
50. K. Andrews, C. Heegard, and D. Kozen, "Interleaver design methods for turbo codes," in Proc. 1998 IEEE Int. Symp. Information Theory, p. 420.
51. M. Campanella, G. Garbo, and S. Mangione, "Simple method of limiting the delay of optimized interleavers for turbo-codes," Electron. Lett., vol. 36, no. 14, pp. 1216-1217, Jul. 2000.
52. G. Carbo and S. Mangione, "Some results on delay-constrained interleavers for turbo codes," in Proc. SoftCom 2001 Workshop Channel Coding Techniques, pp. 17-24.
53. S. Crozier, "New high-spread high-distance interleavers for turbo codes," in Proc. 20th Biennial Symp. Communications, 2000, pp. 3-7.
54. S. Crozier, J. Lodge, P. Guinand, and A. Hunt, "Performance of turbo codes with relative prime and golden interleaving strategies," in Proc. 6th Int. Mobile Satellite Conf. (IMSC'99), pp. 268-275.
55. S. Crozier and P. Guinand, "Distance bounds and the design of high distance interleavers for turbo codes," in Proc. 21st Biennial Symp. Communications, 2002, pp. 10-14.
56. S. Crozier and P. Guinand, "Distance upper bounds and true minimum distance results for turbo codes designed with DRP interleavers," in Proc. Int. Symp. Turbo Codes, 2003, pp. 169-172.
57. O. Y. Takeshita, "Permutation polymonimal interleavers: An algebraic-geometric perspective," IEEE Trans. Inf. Theory, vol. 53, no. 6, pp. 2116-2132, Jun. 2007.
58. J. Sun and O. Y. Takeshita, "Interleavers for turbo codes using permutation polynomial over integer rings," IEEE Trans. Inf. Theory, vol. 51, no. 1, pp. 101-119, Jan. 2005.
59. O. Y. Takeshita and D. J. Costello, Jr., "New deterministic interleaver designs for turbo codes," IEEE Trans. Inf. Theory, vol. 46, no. 6, pp. 1988-2006, Sep. 2000.
60. C. J. Corrada-Bravo and I. Rubio, "Deterministic interleavers for turbo codes with random-like performance and simple implementation," presented at the 3rd Int. Symp. Turbo Codes, Brest, France, 2003.
61. A. Hunt, S. Crozier, M. Richards, and K. Gracie, "Performance degradation as a function of overlap depth when using sub-block processing in the decoding of turbo codes," presented at the Int. Mobile Satellite Conf. (IMSC), Ottawa, ON, Canada, 1999.
62. S. Crozier and P. Guinand, "Distance upper bounds and true minimum distance results for turbo-codes designed with DRP interleavers," Ann. Telecommun., pp. 1-28, Jan./Feb. 2005.
63. F. Jiang, E. Psota, and L. C. Pérez, "The generator and parity-check matrices of turbo codes," presented at the Conf. Information Sciences and Systems, Princeton, NJ, 2006.
64. D. J. C. MacKay, "Good error-correcting codes based on very sparse matrices," IEEE Trans. Inf. Theory, vol. 45, no. 2, pp. 399-431, Mar. 1999.
65. D. Divsalar, H. Jin, and R. McEliece, "Coding theorems for turbo-like codes," presented at the 36th Annu. Allerton Conf. Communication, Control, and Computing, Monticello, IL, 1998.
66. H. Jin, A. Khandekar, and R. McEliece, "Irregular repeat accumulate codes," in Proc. 2nd Int. Symp. Turbo Codes, 2000, pp. 1-8.
67. A. Abbasfar, D. Divsalar, and K. Yao, "Accumulate repeat accumulate codes," in Proc. 2004 Int. Symp. Information Theory, p. 505.
68. M. M. Mansour and N. R. Shanbhag, "Turbo decoder architectures for low-density parity-check codes," in Proc. Global Telecommunications Conf., 2002, vol. 2, pp. 1383-1388.
69. R. J. McEliece, D. J. C. MacKay, and J.-F. Cheng, "Turbo decoding as an instance of pearl's Fbelief propagation-algorithm," IEEE J. Sel. Areas Commun., vol. 16, no. 2, pp. 140-152, Feb. 1998.
70. J. Pearl, Probabilistic Reasoning in Intelligent Systems. San Francisco, CA: Morgan Kaufmann, 1988.
71. N. Wiberg, "Codes and decoding on general graphs," Linköping Studies in Science and Technology, Dissertation 440, Department of Electrical Engineering, Linköping University, Linköping, Sweden, 1996, S-581 83.
72. L. C. Pérez and J. L. Walker, "Graph based codes and decoders," presented at the 2006 American Mathematical Society Conf., New Orleans, LA, 2006.
73. W. J. Blackert, E. K. Hall, and S. G. Wilson, "An upper bound on turbo code free distance," in Proc. Int. Conf. Communications, May 1996, pp. 957-961.