Skip to main content

On the Error Exponents of Reliability-Order-Based Decoding Algorithms for Linear Block Codes

  • Conference paper
Book cover Coding, Cryptography and Combinatorics

Part of the book series: Progress in Computer Science and Applied Logic ((PCS,volume 23))

Abstract

In this paper, for any reliability-order-based decoding algorithm of linear block codes, we prove that the error exponent and the squared error-correction radius are equal to each other. A known method for computing the squared error-correction radius is improved. The improved method can also be used further to compute the effective error coefficient of the reliabilityorder-based decoding algorithms

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G.D. Forney Jr., “Generalized Minimum Distance Decoding,” IEEE Trans. Inform. Theory, vol.IT-12, no. 2, pp. 125–131, April 1966.

    Article  MathSciNet  Google Scholar 

  2. D. Chase, “A Class of Algorithms for Decoding Block Codes with Channel Measurement Information,” IEEE Trans. Inform. Theory, vol. IT-18, no. 1, pp. 170–182, Jan. 1972.

    Article  MathSciNet  Google Scholar 

  3. G.D. Forney Jr., “A Bounded-Distance Decoding Algorithm for the Leech Lattice, with Generalizations,” IEEE Trans. Inform. Theory, vol. 35, no. 4, pp. 906–909, July 1989.

    Article  MathSciNet  Google Scholar 

  4. B. Shen, K.K. Tzeng and C. Wang, “A Bounded-Distance Decoding Algorithm for Binary Linear Block Codes Achieving the Minimum Effective Error Coefficient,” IEEE Trans. Inform. Theory, vol. 42, no. 6, pp. 1987–1991, Nov. 1996.

    Article  MathSciNet  MATH  Google Scholar 

  5. G.D. Forney and A. Vardy, “Generalized Minimum-Distance Decoding of Euclidean Codes and Lattices,” IEEE Trans. Inform. Theory, vol. 42, no. 6, pp. 1992–2026, Nov. 1996.

    Article  MathSciNet  MATH  Google Scholar 

  6. M.P.C. Fossorier and S. Lin, “A Unified Method for Evaluating the Error-Correction Radius of Reliability-Based Soft-Decision Algorithms for Linear Block Codes,” IEEE Trans. Inform. Theory, vol. 44, no. 2, pp. 691–700, Mar. 1998.

    Article  MathSciNet  MATH  Google Scholar 

  7. E. Fishier, O. Amrani and Y. Be’ery, “Geometrical and Performance Analysis of GMD and Chase Decoding Algorithms,” IEEE Trans. Inform. Theory, vol. 45, no. 5, pp. 1406–1422, July 1999.

    Article  MathSciNet  Google Scholar 

  8. T. Kasami, “On Integer Programming Problems Related to Soft-Decision Iterative Decoding Algorithms,” 13th Int. Symp. Proceedings/AAECC 13, Honolulu, Hawaii, USA, pp. 43–54, Nov. 1999.

    MathSciNet  Google Scholar 

  9. Y. Tang, T. Kasami and T. Fujiwara, “On the Computation of the Search Centers and the Evaluation of the Testing Conditions for the h-Chase Decoding,” 23rd Symp. on Inform. Theory & Its Appl., Aso, Kumamoto, Japan, pp. 77–80, Oct. 2000.

    Google Scholar 

  10. Y. Tang, T. Fujiwara and T. Kasami, “Computation of Nearest Boundary Points for Symmetrical Decoding of Linear Block Codes,” Designs, Codes, Graphs and their Links II, Kyoto, Japan, Aug. 2001.

    Google Scholar 

  11. Y. Tang, T. Fujiwara and T. Kasami, “Asymptotic Optimality of the GMD and Chase Decoding Algorithms”, IEEE Trans. Inform. Theory, vol. 48, no. 8, pp. 2401–2405, August 2002.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer Basel AG

About this paper

Cite this paper

Tang, Y. (2004). On the Error Exponents of Reliability-Order-Based Decoding Algorithms for Linear Block Codes. In: Feng, K., Niederreiter, H., Xing, C. (eds) Coding, Cryptography and Combinatorics. Progress in Computer Science and Applied Logic, vol 23. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7865-4_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-7865-4_21

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9602-3

  • Online ISBN: 978-3-0348-7865-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics