Skip to main content
SpringerLink
Log in

Subcodes of Reed-Solomon Codes Suitable for Soft Decoding

  • Conference paper
Book cover Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4851))

  • 915 Accesses

Abstract

Reed-Solomon (RS) codes over GF(2m) have traditionally been the most popular non-binary codes in almost all practical applications. The distance properties of RS codes result in excellent performance under hard-decision bounded-distance decoding. In this work, we consider certain subcodes of RS codes over GF(q m) whose q-ary traces are BCH codes over GF(q). The properties of these subcodes are studied and low-complexity hard-decision and soft-decision decoders are proposed. The decoders are analyzed, and their performance is compared with that of comparable RS codes. Our results suggest that these subcodes of RS codes could have some advantages when compared to RS codes.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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. Reed, I.S., Solomon, G.: Polynomial codes over certain finite fields. J. SIAM 8, 300–304 (1960)

    MATH  MathSciNet  Google Scholar 

  2. Guruswami, V., Sudan, M.: Improved decoding of Reed-Solomon and algebraic-geometry codes. IEEE Trans. on Info. Theory 45(6), 1757–1767 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. Koetter, R., Vardy, A.: Algebraic Soft-decision Decoding of Reed-Solomon Codes. IEEE Trans. Inform. Theory 49(11), 2809–2825 (2003)

    Article  MathSciNet  Google Scholar 

  4. Forney, D.: Generalized Minimum Distance Decoding. IEEE Trans. Inform. Theory 12(2), 125–131 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  5. Vardy, A., Beery, Y.: Bit-level Soft-decision Decoding of Reed-Solomon Codes. IEEE Trans. on Comm. 39(3), 440–444 (1991)

    Article  MATH  Google Scholar 

  6. Ponnampalam, V., Vucetic, B.: Soft Decision Decoding of Reed-Solomon Codes. IEEE Trans. on Comm. 50(11), 1758–1768 (2002)

    Article  Google Scholar 

  7. Jiang, J., Narayanan, K.R.: Iterative Soft Decoding of Reed-Solomon Codes. IEEE Commun. Lett. 8(4), 244–246 (2004)

    Article  Google Scholar 

  8. MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North-Holland, The Netherlands, Amsterdam (1977)

    MATH  Google Scholar 

  9. Augot, D., Charpin, P., Sendrier, N.: Studying the Locator Polynomials of Minimum Weight Codewords of BCH Codes. IEEE Trans. Inform. Theory 38(3), 960–973 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ashikhmin, A., Litsyn, S.: Simple MAP Decoding of First-Order Reed-Muller and Hamming Codes. IEEE Trans. Inform. Theory 50(8), 1812–1818 (2004)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India

    Safitha J. Raj & Andrew Thangaraj

Authors
  1. Safitha J. Raj
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrew Thangaraj
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Serdar Boztaş Hsiao-Feng (Francis) Lu

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Raj, S.J., Thangaraj, A. (2007). Subcodes of Reed-Solomon Codes Suitable for Soft Decoding. In: Boztaş, S., Lu, HF.(. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2007. Lecture Notes in Computer Science, vol 4851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77224-8_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-77224-8_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77223-1

  • Online ISBN: 978-3-540-77224-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation