Graph Decoding of Array Error-Correcting Codes

  • Patrick G. Farrell
  • Seyed H. Razavi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1746)


The motivation for this paper is to report on concepts and results arising from the continuation of a recent study [1] of graph decoding techniques for block error-control (detection and correction) codes. The representation of codes by means of graphs, and the corresponding graph-based decoding algorithms, are described briefly. Results on the performance of graph decoding methods for block codes of the array and generalised array type will be presented, confirming the illustrative examples given in [1]. The main novel result is that the (7,4) Generalised Array Code, equivalent to the (7,4) Hamming Code, which has a graph which contains cycles, can be successfully decoded by means of an iterated min-sum algorithm.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    P.G. Farrell: Graph Decoding of Error-Control Codes; 5th Int. Symposium on DSP for Communication Systems, Scarborough, Perth, Australia, 1–4 February, 1999.Google Scholar
  2. [2]
    R.M. Tanner: A Recursive Approach to Low-Complexity Codes; IEEE Trans Info Theory, Vol IT-27,No 5, pp533–547, Sept 1981.CrossRefMathSciNetGoogle Scholar
  3. [3]
    R.G. Gallager: Low-Density Parity-Check Codes; IRE Trans Info Theory, Vol IT-8,No 1, pp 21–28, Jan 1962.CrossRefMathSciNetGoogle Scholar
  4. [4]
    N. Wiberg, H.-A. Loeliger & R. Kotter: Codes and Iterative Decoding on General Graphs; Euro Trans Telecom, Vol 6, pp513–526, SEPT 1995.CrossRefGoogle Scholar
  5. [5]
    N. Wiberg: Codes and Decoding on General Graphs; PhD Dissertation, Linkoping University, Sweden, April 1996.Google Scholar
  6. [6]
    G.D. Forney: On Iterative Decoding and the Two-Way Algorithm; Int Symp on Turbo Codes, Brest, France, Sept 3–5, 1997.Google Scholar
  7. [7]
    P.G. Farrell: On Generalised Array Codes; in Communications Coding and Signal Processing, Eds B. Honary, M. Darnell and P.G. Farrell, Research Studies Press, 1997.Google Scholar
  8. [8]
    H.-A. Loeliger, F. Tarkoy, F. Lustenberger & M. Helfenstein: Decoding in Analog VLSI; IEEE Comms Mag, April 1999, pp 99–101.Google Scholar
  9. [9]
    I. Martin & B. Honary: Two-Stage Trellis Decoding of the Nordstrom-Robinson Code Based on the Twisted Squaring Construction, submitted to IEE Proceedings-Communications.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Patrick G. Farrell
    • 1
  • Seyed H. Razavi
    • 2
  1. 1.Lancaster UniversityUK
  2. 2.Curtin University of TechnologyPerthAustralia

Personalised recommendations