ETRI Journal

Electronics and Telecommunications Research Institute (한국전자통신연구원)
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General Log-Likelihood Ratio Expression and Its Implementation Algorithm for Gray-Coded QAM Signals

  • Kim, Ki-Seol (Department of Electronics and Computer Engineering, Hanyang University) ;
  • Hyun, Kwang-Min (Department of Information and Communication Engineering, Wonju National College) ;
  • Yu, Chang-Wahn (Mobile Telecommunication Research Division, ETRI) ;
  • Park, Youn-Ok (Mobile Telecommunication Research Division, ETRI) ;
  • Yoon, Dong-Weon (Department of Electronics and Computer Engineering, Hanyang University) ;
  • Park, Sang-Kyu (Department of Electronics and Computer Engineering, Hanyang University)
  • Received : 2005.08.30
  • Published : 2006.06.30
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Abstract

A simple and general bit log-likelihood ratio (LLR) expression is provided for Gray-coded rectangular quadrature amplitude modulation (R-QAM) signals. The characteristics of Gray code mapping such as symmetries and repeated formats of the bit assignment in a symbol among bit groups are applied effectively for the simplification of the LLR expression. In order to reduce the complexity of the max-log-MAP algorithm for LLR calculation, we replace the mathematical max or min function of the conventional LLR expression with simple arithmetic functions. In addition, we propose an implementation algorithm of this expression. Because the proposed expression is very simple and constructive with some parameters reflecting the characteristic of the Gray code mapping result, it can easily be implemented, providing an efficient symbol de-mapping structure for various wireless applications.

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