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In this work, the design of robust, protograph-based low-density parity-check(LDPC) codes for rate-adaptive communication via probabilistic shaping isconsidered. Recently, probabilistic amplitude shaping (PAS) by B\"ocherer etal. has been introduced for capacity approaching and rate-adaptivecommunication with a bitwise-demapper and binary decoder. Previous work by theauthors considered the optimization of protograph based LDPC codes for PAS andspecific spectral efficiencies (SEs) to jointly optimize the LDPC code nodedegrees and the mapping of the coded bits to the bit-interleaved codedmodulation (BICM) bit-channels. We show that these codes tend to perform poorwhen operated at other rates and propose the design of robust LDPC codes byemploying a min-max approach in the search for good protograph ensembles viadifferential evolution. The considered design uses a single 16amplitude-shift-keying (ASK) constellation and a robust 13/16 rate LDPC code tooperate between 0.7 to 2.7 bits per channel use. For a blocklength of 16224bits and a target frame error rate of 1e-3 the proposed code operates within1.32 dB of continuous AWGN capacity for 0.7 to 1.3 bpcu and within 1.05 dB for1.3 bpcu to 2.7 bpcu.

Design of Robust, Protograph Based LDPC Codes for Rate-Adaptation via Probabilistic Shaping