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 lowdensity parity check code of the same average rate as that induced by our simple padding.

For Gaussian channels with peak and average power constraints the optimal modulation (OM) schemes are known to have nonuniform probability distributions over the signal points. An established way to obtain these distributions is assigning different number of bits to different constellation points. However, this method leads to challenges in demodulation as if a symbol is identified falsely, due to the different bit lengths of symbols, bit insertions or deletions may occur which may in return cause error propagation. Hence, the difficulty of realizing the channel optimal distributions on constellation signals impeded OM from becoming widely utilized in communication systems. In this thesis, we propose a practical system for OM that uses only a simple padding scheme instead of the complex mechanisms in the current literature. A guess-based error correction demodulator lies at the core of the proposed system. Together with the padding scheme of our choice, our novel light-weight variant of Guessing Random Additive Noise Decoding (GRAND) demodulator protects the system against insertions and deletions. We display that with our approach an overall gain of up to 2 dB in energy per bit over noise spectral density (𝐸 𝑏 /𝑁 0 ) is achievable compared to Quadrature Amplitude Modulation (QAM) with the same number of points.