Application of bubble-check algorithm to non-binary LLR computation in QAM coded schemes

The generation of intrinsic LLR messages in non-binary (NB) coded schemes associated with quadrature amplitude modulation (QAM) is considered. It is shown that the intrinsic LLR message generation corresponds to the same kind of computation as the one performed at the elementary check nodes in extended min-sum NB-LDPC decoders, i.e. finding a given number of minimum values in a structured set. It is proposed 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 steps.