  Optimal modulation (OM) schemes for Gaussian channels with peak and average
power constraints are known to require nonuniform probability distributions
over signal points, which presents practical challenges. An established way to
map uniform binary sources to non-uniform symbol distributions is to assign a
different number of bits to different constellation points. Doing so, however,
means that erroneous demodulation at the receiver can lead to bit insertions or
deletions that result in significant binary error propagation. In this paper,
we introduce a light-weight variant of Guessing Random Additive Noise Decoding
(GRAND) to resolve insertion and deletion errors at the receiver by using a
simple padding scheme. Performance evaluation demonstrates that our approach
results in an overall gain in demodulated bit-error-rate of over 2 dB Eb/N0
when compared to 128-Quadrature Amplitude Modulation (QAM). The GRAND-aided OM
scheme outperforms coding with a low-density parity check code of the same
average rate as that induced by our simple padding.
