Fast and reduced-complexity decoding rule for q-ary LDPC codes by using the duality properties

Alaa Ghaith, Joseph Boutros, Yuan Wu Yi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The paper studies symbol-by-symbol maximum a posteriori (MAP) decoding algorithms for non binary codes over an extension field GF(q). This decoding rule minimizes the probability of symbol error over a time-discrete memory less channel by employing the dual code. It is shown that these algorithms meet all requirements needed for iterative decoding as the output of the decoder can be split into three independent estimates: soft channel value, a priori term and extrinsic value. It represents a better form of coding for the Q-ary LDPC codes, which have been shown to outperform binary LDPC codes and Reed-Solomon codes on the AWGN channel and it gives us a new fast and reduced-complexity decoding algorithm. The complexity of this rule varies inversely with code rate, making the technique particularly attractive for high rate codes. Finally, we see that complexity is reduced by using the dual code, and the algorithm is accelerated by using the Fast Hadamard Transform (FHT). Examples are given for both single parity check (non iterative case) and LDPC (iterative case) non binary codes.

Original languageEnglish
Title of host publicationIEEE International Conference on Wireless and Mobile Computing, Networking and Communications 2006, WiMob 2006
Pages221-228
Number of pages8
DOIs
Publication statusPublished - 1 Dec 2006
EventIEEE International Conference on Wireless and Mobile Computing, Networking and Communications 2006, WiMob 2006 - Montreal, QC, United States
Duration: 19 Jun 200621 Jun 2006

Publication series

NameIEEE International Conference on Wireless and Mobile Computing, Networking and Communications 2006, WiMob 2006

Other

OtherIEEE International Conference on Wireless and Mobile Computing, Networking and Communications 2006, WiMob 2006
CountryUnited States
CityMontreal, QC
Period19/6/0621/6/06

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Keywords

  • A posteriori probability (APP)
  • Dual codes
  • Fast Hadamard Transform (FHT)
  • Iterative decoding
  • Low Density Parity Check (LDPC) codes
  • Single Parity Check (SPC) codes

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Hardware and Architecture
  • Software

Cite this

Ghaith, A., Boutros, J., & Yi, Y. W. (2006). Fast and reduced-complexity decoding rule for q-ary LDPC codes by using the duality properties. In IEEE International Conference on Wireless and Mobile Computing, Networking and Communications 2006, WiMob 2006 (pp. 221-228). [1696346] (IEEE International Conference on Wireless and Mobile Computing, Networking and Communications 2006, WiMob 2006). https://doi.org/10.1109/WIMOB.2006.1696346