This Letter considers the generation of intrinsic LLR messages in non-binary coded schemes associated to QAM modulation. We show that intrinsic LLR message generation corresponds to the same kind of computation than the one performed at the elementary check nodes in Extended Min-Sum non-binary LDPC decoders, i.e. finding a given number of minimum values in a structured set. We propose to use the Bubble-Check algorithm for the LLR calculation to benefit from two advantages: low-complexity hardware architecture and sharing the same hardware at the demapping and the decoding step. Introduction: Non-binary (NB) coded schemes can be naturally associated to high-order modulation for high data rate, leading to low-error high-spectral-efficiency communication systems. Compared to binary coded schemes, the use of NB codes improves the performance of the decoding algorithms [1] [2] as the intrinsic likelihoods of the received symbols (which are the inputs to the decoder) are uncorrelated from one symbol to another. Recent work on QAM binary soft demapping include [3]. Figure 1 presents the schematics of the considered digital communication chain. Information data are encoded by a NB encoder and then mapped to a symbol in the QAM constellation. Note that the order of the NB code, q, corresponds to the number of signals in the modulation, M (i.e. M = q). After the channel, the modulated noisy symbols are demapped to generate the intrinsic message. Note that this Letter focusses on the demapper block and considers the generation of the intrinsic likelihood messages. Even if our approach may be considered for any NB coded modulation scheme that needs the sorting of elements in the likelihood vector, we essentially focus on NB-LDPC and Extended Min-Sum (EMS) [4] decoding algorithms 1 . Fig. 1. Digital communication chain