Coding for parallel channels: Gallager bounds and applications to turbo-like codes

IEEE Transactions on Information Theory

Volumn 53, Issue 7, 2007, Pages 2394-2428

  Sason, Igal ^a   Goldenberg, Idan ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Accumulate repeat accumulate codes; Distance spectrum; Input output weight enumerator (IOWE); Iterative decoding; Linear codes; Maximum likelihood (ML) decoding; Memoryless binary input output symmetric (MBIOS) channels; Parallel channels

Indexed keywords

ACCUMULATE-REPEAT-ACCUMULATE CODES; INPUT-OUTPUT WEIGHT ENUMERATOR; MEMORYLESS BINARY-INPUT OUTPUT-SYMMETRIC (MBIOS) CHANNELS; PARALLEL CHANNELS;

BLOCK CODES; ERRORS; MAXIMUM LIKELIHOOD; PROBABILITY; TURBO CODES;

ITERATIVE DECODING;

EID: 34447316708     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2007.899543     Document Type: Article

References (39)

1. A. Abbasfar, D. Divsalar, and K. Yao, "Accumulate-repeat-accumulate codes," IEEE Trans. Commun., vol. 55, no. 4, pp. 692-702, Apr. 2007.
2. A. Abbasfar, K. Yao, and D. Divsalar, "Maximum-likelihood decoding analysis of accumulate-repeat-accumulate codes," in Proc. IEEE 2004 Global Telecommunications Conf. (GLOBECOM 2004), Dallas, TX, Dec. 2004, pp. 514-519.
3. E. Agrell, "Voronoi regions for binary linear block codes," IEEE Trans. Inf. Theory, vol. 42, no. 1, pp. 310-316, Jan. 1996.
4. S. Benedetto and G. Montorsi, "Unveiling turbo codes: Some results on parallel concatenated coding schemes," IEEE Trans. Inf. Theory, vol. 42, no. 2, pp. 409-429, Mar. 1996.
5. S. Benedetto, D. Divsalar, G.Montorsi, and F. Pollara, "Serial concatenation of interleaved codes: Performance analysis, design and iterative decoding," IEEE Trans. Inf. Theory, vol. 44, no. 3, pp. 909-926, May 1998.
6. D. Burshtein and G. Miller, "Asymptotic enumeration methods for analyzing LDPC codes," IEEE Trans. Inf. Theory, vol. 50, no. 6, pp. 1115-1131, Jun. 2004.
7. J. W. Craig, "A new, simple and exact result for calculating the probability of error for two-dimensional signal constellations," in Proc. 1991 IEEE Global Communications Conf. (GLOBECOM 1991), Boston, MA, 1991, pp. 25.5.1-25.5.5.
8. C. Di, T. Richardson, and R. Urbanke, "Weight distribution of low-density parity-check codes," IEEE Trans. Inf. Theory, vol. 52, no. 11, pp. 4839-4855, Nov. 2006.
9. D. Divsalar, H. Jin, and R. J. McEliece, "Coding theorems for 'turbolike' codes," in Proc. 36th Allerton Conf. Communication, Control, and Computing, Monticello, IL, Sep. 1998, pp. 201-210.
10. D. Divsalar, "A simple tight bound on error probability of block codes with application to turbo codes,"NASA, Jet Propulsion Lab., Pasadena, CA, Nov. 15, 1999, pp. 1-35, Telecommunications and Mission Operations (TMO) Progr. Rep. 42-139 Online. Available: http://tmo.jpl.nasa.gov/tmo/progress_report/42-139/139L.pdf
11. T. M. Duman, "Turbo codes and turbo coded modulation systems: Analysis and performance bounds," Ph.D. dissertation, Elect. Comput. Eng. Dep., Northeastern Univ., Boston, MA, 1998.
12. T. M. Duman and M. Salehi, "New performance bounds for turbo codes," IEEE Trans. Commun., vol. 46, no. 6, pp. 717-723, Jun. 1998.
13. P. M. Ebert, "Error bounds for parallel communication channels" Ph.D. dissertation, MIT, Cambridge, MA, 1966.
14. R. G. Gallager, Low-Density Parity-Check Codes. Cambridge, MA: MIT Press, 1963.
15. R. G. Gallager, Information Theory and Reliable Communications. New York: Wiley, 1968.
16. A. Guillen i Fabregas and G. Caire, "Coded modulation in the block-fading channel: Coding theorems and code construction," IEEE Trans. Inf. Theory, vol. 52, no. 1, pp. 91-114, Jan. 2006.
17. J. Ha, J. Kim, and S. W. McLaughlin, "Rate-compatible puncturing of low-density parity-check codes," IEEE Trans. Inf. Theory, vol. 50, no. 11, pp. 2824-2836, Nov. 2004.
18. C. H. Hsu and A. Anastasopoulos, "Asymptotic weight distributions of irregular repeat-accumulate codes," in Proc. 2005 IEEE Global Telecommunications Conf. (GLOBECOM 2005), St. Louis, MO, Nov. 2005, vol. 3, pp. 1147-1151.
19. H. Jin and R. J. McEliece, "RA codes achieve AWGN channel capacity," in Proc. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 13th Int. Symp. (AAECC-13), Honolulu, HI (Lecture Notes in Computer Science), M. Fossorier, H. Imai, S. Lin, and A. Poli, Eds. Heidelberg, Germany: Springer-Verlag, 1999, vol. 1719, pp. 10-18.
20. H. Jin and R. J. McEliece, "Irregular repeat-accumlate codes," in Proc. 2nd Int. Conf. Turbo Codes and Related Topics, Brest, France, Sep. 2000, pp. 1-8.
21. H. Jin and R. J. McEliece, "Coding theorems for turbo code ensembles," IEEE Trans. Inf. Theory, vol. 48, no. 6, pp. 1451-1461, Jun. 2002.
22. A. Khandekar, "Graph-based codes and iterative decoding" Ph.D. dissertation, California Inst. Technol., Pasadena, CA, 2002.
23. R. Liu, P. Spasojevic, and E. Soljanin, "Reliable channel regions for good binary codes transmitted over parallel channels," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1405-1424, Apr. 2006.
24. S. Litsyn and V. Shevelev, "Distance distributions in ensembles of irregular low-density parity-check codes," IEEE Trans. Inf. Theory vol. 49, no. 12, pp. 3140-3159, Dec. 2003.
25. R. J. McEliece, "How to compute weight enumerators for convolutional codes," in Communications and Coding, ser. Tauton Research Studies, M. Darnel and B. Honary, Eds. New York: Wiley, 1998, pp. 121-141.
26. G. Miller and D. Burshtein, "Bounds on the maximum-likelihood decoding error probability of low-density parity-check codes," IEEE Trans. Inf. Theory, vol. 47, no. 7, pp. 2696-2710, Nov. 2001.
27. L. C. Perez, J. Seghers, and D. J. Costello, "A distance spectrum interpretation of turbo codes," IEEE Trans. Inf. Theory, vol. 42, no. 6, pp. 1698-1709, Nov. 1996.
28. H. D. Pfister, I. Sason, and R. Urbanke, "Capacity-achieving ensembles for the binary erasure channel with bounded complexity," IEEE Trans. Inf. Theory, vol. 51, no. 7, pp. 2352-2379, Jul. 2005.
29. H. D. Pfister and I. Sason, "Accumulate-repeat-accumulate codes: Capacity-achieving ensembles of systematic codes for the erasure channel with bounded complexity," IEEE Trans. Inf. Theory, vol. 53, no. 6, pp. 2088-2115, Jun. 2007.
30. G. Poltyrev, "Bounds on the decoding error probability of binary linear codes via their spectra," IEEE Trans. Inf. Theory, vol. 40, no. 4, pp. 1284-1292, Jul. 1994.
31. I. Sason and S. Shamai (Shitz), "Gallager's 1963 Bound: Extensions and Observations," Technion, Haifa, Israel, 1998, Tech. Rep. CC No. 258 Online. Available: http://www.ee.technion.ac.il/people/sason/ CC258_{text, figures}.pdf
32. I. Sason and S. Shamai (Shitz), "On improved bounds on the decoding error probability of block codes over interleaved fading channels, with applications to turbo-like codes," IEEE Trans. Inf. Theory, vol. 47, no. 6, pp. 2275-2299, Sep. 2001.
33. I. Sason and S. Shamai (Shitz), "Performance analysis of linear codes under maximum-likelihood decoding: A tutorial," in Foundations and Trends in Communications and Information Theory. Delft, The Netherlands: NOW Pub., 2006, vol. 3, pp. 1-222.
34. I. Sason, E. I. Telatar, and R. Urbanke, "On the asymptotic input-output weight distributions and thresholds of convolutional and turbo-like encoders," IEEE Trans. Inf. Theory, vol. 48, no. 12, pp. 3052-3061, Dec. 2002.
35. I. Sason and G. Wiechman, "On achievable rates and complexity of LDPC codes over parallel channels: Bounds and applications," IEEE Trans. Inf. Theory, vol. 53, no. 2, pp. 580-598, Feb. 2007.
36. S. Shamai (Shitz) and I. Sason, "Variations on the Gallager bounds, connections and applications," IEEE Trans. Inf. Theory, vol. 48, no. 12, pp. 3029-3051, Dec. 2002.
37. N. Shulman and M. Feder, "Random coding techniques for nonrandom codes," IEEE Trans. Inf. Theory, vol. 45, no. 6, pp. 2101-2104, Sep. 1999.
38. X. Wu, H. Xiang, and C. Ling, "New Gallager bounds in block-fading channels," IEEE Trans. Inf. Theory, vol. 53, no. 2, pp. 684-694, Feb. 2007.
39. J. Zheng and S. L. Miller, "Performance analysis of coded OFDM systems over frequency-selective fading channels," in Proc. 2003 IEEE Global Telecommunications Conf. (GLOBECOM '03), San Francisco, CA, Dec. 2003, pp. 1623-1627.