A communication system in which a constellation employing partially anti-symmetric amplitude labels is used to transmit probabilistically shaped amplitudes such that said amplitudes are also used to determine the signs applied thereto for transmission. In an example embodiment, a data transmitter is configured to use a suitable logic function (e.g., an XOR function) to place the parity generated by an FEC code into a selected amplitude bit while using the partially anti-symmetric amplitude labels to avoid placing the parity into the sign bits of the transmitted constellation symbols. In some embodiments, the FEC code can be a low-density parity-check code. Some embodiments are compatible with layered FEC coding, e.g., employing an outer FEC code and an inner FEC code. In some embodiments, FEC coding may be optional. Some embodiments can advantageously be used in communication systems relying on DMT modulation, such as the systems providing DSL access over copper wiring.