It's tricky because as noise increases, large constellations, although perhaps in theory with advanced statistical decoding (where you consider P(Symbol|Receive

It's tricky because as noise increases, large constellations, although perhaps in theory with advanced statistical decoding (where you consider P(Symbol|Received signal)) they're advantageous, become less viable and more demanding computationally. Usually the gains are a small factor. At one point, the energy cost of computation required to make statistical decoding[1] surpasses any gains from increases in complexity. More than that, the ratio of channel energy (or cost) requirement to computational energy can vary :) For example, if you're transmitting a message to a space probe, the energy and costs associating with message transmission are enormous, such that the decoding energy will be a lower proportion (favoring more complex decoding systems). For a computer bus transmitting signals internally at short distances, the energy cost of encoding (and even using QAM or non-binary encoding at all) and statistical decoding will probably be less than the energy gains. Credit to Christopher Blake et. al in this paper: (as seen on Canadian Workshop on Information Theory :) ) https://tspace.library.utoronto.ca/bitstream/1807/69482/1/IT-13-0964.R1.pdf https://tspace.library.utoronto.ca/bitstream/1807/69482/1/IT... From the abstract: "This implies that the average energy per decoded bit must approach infinity for any sequence of decoders that approaches capacity" (valid for the VLSI model in question, and binary channel model, but I'd guess this generalizes to any physical computational medium)[2] It's really interesting how in the context more complex isn't always better. [1] Usually the complexity of the whole system, in more practical terms, is determinant as well -- because engineering and maintaining complex systems is difficult [2] More precisely: "It is shown that for any sequence of increasing-block-length decoder circuits implemented according to this model, if the probability of block error is asymptotically less than 1/2 then the energy of the computation scales at least as Ω (n√log n), and so the energy of decoding per bit must scale at least as Ω (√log n)"