LDPC coded QAM signaling: Mapping and Shaping

In this survey, recently proposed techniques to match error-correcting codes (ECC) with unshaped and shaped QAM signaling are reviewed. The analysis of ECCs used in conjunction with modulation and shaping is presented. An upper bound on the maximum-likelihood (ML) decoding error probability for the ECC used with (unshaped/shaped) QAM signaling for specific code symbol-to-signal point mappings is derived.The main focus in this work is non-binary (NB) low-density parity-check (LDPC) coded QAM signaling. Simulation results for the frame error rate (FER) performance of belief-propagation (BP) decoding of the practical NB (quasi-cyclic) QC-LDPC codes used with various mappings are compared to the upper bound on the ML decoding error probability.Two variants of shaping used with coded QAM signaling called shaping before coding (SBC) and shaping after coding (SAC) are explored. Simulation results for the FER performance of BP decoding of the NB QC-LDPC codes used with SBC and SAC QAM signaling are compared to the corresponding upper bounds on the ML decoding error probabilities.