Shaping for NB QC-LDPC Coded QAM Signals

An approach to introducing shaping in conjunction with nonbinary (NB) low-density parity-check (LDPC) coded QAM signaling is considered. An algorithm for shaping book optimization is proposed for shaping performed after coding (SAC). The new approach is verified by applying it to the NB quasi-cyclic (QC)-LDPC codes optimized for the communication system with unshaped QAM signaling. Simulation results for the frame error rate (FER) of belief-propagation (BP) decoding for the optimized NB QC-LDPC codes used with shaping before coding (SBC) and SAC with optimized shaping books are presented. They are compared to a random coding bound on the ML decoding error probability for the ensemble of NB LDPC codes used with SAC and simulation results for the binary QCLDPC block codes in the 5G and WiFi standards.