Protograph-Based LDPC Code Design for Shaped Bit-Metric Decoding

Abstract

A protograph-based low-density parity-check (LDPC) code design technique for bandwidth-efficient coded modulation with probabilistic shaping is presented. The approach jointly optimizes the LDPC code node degrees and the mapping of the coded bits to the bit-interleaved coded modulation (BICM) bit-channels. For BICM with uniform inputs and for BICM with probabilistic shaping, binary-input symmetric-output surrogate channels for the code design are used. The constructed codes for uniform inputs perform as good as the multi-edge type codes of Zhang and Kschischang (2013). For 8-ASK and 64-ASK with probabilistic shaping, codes of rates 2/3 and 5/6 with blocklength 64800 are designed, which operate within 0.63 and 0.69 dB of $\frac{1}{2}\,\log_2(1+\text{SNR})$ for a target frame error rate of $10^{-3}$ at spectral efficiencies of 1.38 and 4.25 bits/channel use, respectively.