Bitwise Decomposition of M-QAM Signals

In this paper, we present a simple and general bitwise decomposition expression using log likelihood ratio (LLR) of an arbitrary gray coded rectangular M-QAM signal. Based on the max-log MAP algorithm, we replace the mathematical max or min functions of the conventional LLR expression with simple arithmetic functions associated with given parameters such as a received symbol value and distance between symbols on a signal space. Since the derived LLR expression can be used as a soft bit metric for input to a conventional binary turbo decoder, it is suitable for practical applications with a turbo decoder or other related applications as an alternative to conventional methods