1. A method for selecting a sequence of signal points from a 4-dimensional (4D) QAM constellation to represent a sequence of input bits, the constellation having four phase synmmetries, the method comprising the steps of: applying, during each 4D signaling interval, a first portion of the input bits to a rate-4/5 trellis encoder which transitions from a present state to a next state and generates trellis encoded bits; selecting, in response to the trellis encoded bits, one of a plurality of subsets of the 4D constellation; identifying, in response to a second portion of the input bits, a 4D signal point from the selected subset; generating an output signal representing a valid sequence of successive identified 4D signal points, and wherein a valid sequence of signal points becomes another valid sequence of signal points after a 90, 180, or 270 degree rotation; the plurality of subsets form first and second families of subsets, each family of subsets being evenly divided into a plurality of groups of subsets having four subsets in each group, the subsets within each group being obtainable from each other through 90 degree phase rotations; the trellis encoder occupies one of a plurality of states, the plurality of states being divided into first and second categories, and from each present state, half of the transitions will lead to next states in the first category and half of the transitions will lead to next states in the second category; the subsets that are associated with state transitions from present states in the first category belong to the first family and the subsets that are associated with state transitions from present states in the second category belong to the second family; and for each group of subsets that is associated with state transitions from a present state, two subsets of the group are associated with state transitions from a present state to next states in the first category and two subsets of the group are associated with state transitions from a present state to next states in the second category.