Low complexity LLR metrics for polar coded QAM

This paper presents a low-complexity approach for calculating soft decision metrics of polar coded quadrature amplitude modulation (QAM) system. A simple and general bit log likelihood ratio (LLR) expression is provided for Gray coded 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 exploited effectively for the simplification of the LLR expression. To reduce the complexity of the max-log-MAP algorithm for LLR calculation, these LLRs can be simplified even further by replacing the mathematical min function of the conventional LLR expression with simple arithmetic functions. We introduce supplemental approximation to the max-log-MAP algorithm by averaging the LLR values in different regions to get a single approximate expression. Over AWGN and Rayleigh fading channels, simulation results and complexity analysis demonstrate that the proposed demapper approaches traditional approximations in terms of BER performance, but with much lower low complexity.