Methods for assigning codewoods to points in hexagonal constellations in digital communication systems

A device comprising:

• a transmitter;
• at least one antenna coupled to the transmitter for transmitting a signal over a wireless channel;
• a processor, coupled to the transmitter;
• a computer-readable medium including computer-readable instructions stored therein that, upon execution by the processor, perform operations comprising:
• modeling an hexagonal constellation as a two-dimensional trellis with an horizontal axis varying across a plurality of constellation points and a vertical axis varying across a plurality of codewords [0, 1, . . . , N−1];
• finding a best path through the trellis to select a single constellation point where a codeword from the plurality of codewords is to be assigned in the transition across the trellis diagram, at each state, a current score and the best path that leads to the state is stored in a memory;
• assigning each codeword of the plurality of codewords to the selected constellation point from the plurality of constellation points for a hexagonal constellation;
• and
• using the hexagonal constellation for transmitting data.

A computer program product of computer-readable instructions, tangibly embodied on a non-transitory computer-readable medium and executable by a digital data processor to perform actions directed toward transmitting a signal, the computer-readable instructions configured to cause a device to:

• modeling an hexagonal constellation as a two-dimensional trellis with an horizontal axis varying across a plurality of constellation points and a vertical axis varying across a plurality of codewords [0, 1, . . . , N−1];
• finding a best path through the trellis to select a single constellation point where a codeword from the plurality of codewords is to be assigned in the transition across the trellis diagram, at each state, a current score and the best path that leads to the state is stored in a memory;
• assigning each codeword of the plurality of codewords to the selected constellation point from the plurality of constellation points for a hexagonal constellation;
• and
• using the hexagonal constellation for transmitting data.