Simplified app computation of high order constellations combined with non-binary LDPC decoders

Combining non-binary LDPC (Low-Density Parity-Check) codes and high order constellations, such as Quadrature Amplitude Modulations (QAM), is an effective way to improve the bandwidth efficiency. Since, the message exchanged in the LDPC decoder can be measured by the APP (A Priori Probability) or the LLR (Log-Likelihood Ratio), depending on the decoding algorithm type, the message at the decoder input that computed by the QAM must be using the same calculation. However, the number of operations performed by the QAM increases with the constellation order, and the calculation changes with the channel type. In this paper, we use simplified LLR computations, introduced for binary codes, to simplify the APP calculation of square-QAM-Gray demapping for APPbased non-binary LDPC decoders. Under Gaussian channel, the simplified APP calculation achieves the same performance that obtained with the exact APP computation. The same simplified APP calculation used for a Gaussian channel can be applied, with minor operations added, for Rayleigh channel, and it shows a small performance loss with respect to the exact APP computation. These simplifications simplify the combination of non-binary LDPC codes with QAM. With this method, it is easy to change a decoding algorithm based on the APP to an algorithm based on the LLR