Optimal Modulation

Systems and methods disclose a practical implementation of optimal modulation (OM) for the Complex Additive White Gaussian Noise (CAWGN) channel. At the sender, we map from uniform distributions of data to non-uniform distributions of points in constellations by using a technique inspired by Huffman codes. We replace Gray codes with a bit mapping suited to our constellations, where different points may map to string of bits of different lengths. At the receiver, we perform distribution-aware detection. The differing lengths of bits for modulation points can used as a simple checking mechanism that, when combined with guessing random additive noise decoding (GRAND), yields bit-error-rate (BER) advantages.