Open AccessGeneral Log‐Likelihood Ratio Expression and Its Implementation Algorithm for Gray‐Coded QAM Signals
Author(s) -
Kim Ki Seol,
Hyun Kwangmin,
Yu Chang Wahn,
Park Youn Ok,
Yoon Dongweon,
Park Sang Kyu
Publication year - 2006
Publication title -
etri journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.295
H-Index - 46
eISSN - 2233-7326
pISSN - 1225-6463
DOI - 10.4218/etrij.06.0105.0161
Subject(s) - gray code , algorithm , qam , quadrature amplitude modulation , expression (computer science) , constructive , computer science , mathematics , bit error rate , decoding methods , process (computing) , programming language , operating system
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.