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The author discusses trellis shaping, a method of selecting a minimum-weight sequence from an equivalence class of possible transmitted sequences by a search through the trellis diagram of a shaping convolutional code C/sub s/. Shaping gains on the order of 1 dB may be obtained with simple four-state shaping codes and with moderate constellation expansion. The shaping gains obtained with more complicated codes approach the ultimate shaping gain of 1.53 dB. With a feedback-free syndrome-former for C/sub s/, transmitted data can be recovered without catastrophic error propagation. Constellation expansion and peak-to-average energy ratio may be effectively limited by peak constraints. With lattice-theoretic constellations, the shaping operation may be characterized as a decoding of an initial sequence in a channel trellis code by a minimum-distance decoder for a shaping trellis code based on the shaping convolutional code, and the set of possible transmitted sequences is then the set of code sequences in the channel trellis code that lie in the Voronoi region of the trellis shaping code.>
G. David Forney (Sun,) studied this question.