Optimal trellis code design for QPSK and higher order quadrature amplitude modulations

A variable data rate Trellis Code Modulation (TCM) encoder comprising:

• a variable rate input that receives at least one input bit each symbol period;
• a Finite State Machine (FSM) receiving two FSM inputs, wherein a first FSM input of the two FSM inputs receives a first input bit of the at least one input but, wherein a second FSM input of the two FSM inputs receives a second input bit of the at least one input bit when present and receives a zero when the second input bit of the at least one input bit is not present, wherein each symbol period the FSM produces an FSM output bit based upon the two FSM inputs;
• a variable rate symbol mapper operably coupled to the variable rate input and to the FSM, wherein the variable rate symbol mapper, for each symbol period, receives the at least one input bit, the FSM output bit, and a mode selection input that selects a constellation of a plurality of supported constellations including a Quadrature Phase Shift Keying (QPSK) constellation and at least one higher order constellation;
• wherein at least the FSM output bit is employed to indicate a plurality of valid constellation points of a selected constellation, wherein the plurality of valid constellation points is a subset of all constellation points of the selected constellation;
• and
• wherein when the mode selection input selects a QPSK constellation, the second input bit is set to zero, the FSM output bit indicates a pair of valid constellation points for the QPSK constellation, and the first input bit selects a constellation point of the pair of valid constellation points as the variable data rate TCM output;
• and
• wherein variable data rate TCM encoder produces TCM codes with optimal Euclidean distance properties for the QPSK constellation and near optimal Euclidian distance properties for the at least one higher order constellation.

A variable data rate Trellis Code Modulation (TCM) encoder comprising:

• a variable rate input that receives at least one input bit each symbol period;
• a Finite State Machine (FSM) receiving two FSM inputs, wherein a first FSM input of the two FSM inputs receives a first input bit of the at least one input but, wherein a second FSM input of the two FSM inputs receives a second input bit of the at least one input bit when present and receives a zero when the second input bit of the at least one input bit is not present, wherein each symbol period the FSM produces an FSM output bit based upon the two FSM inputs;
• a variable rate symbol mapper operably coupled to the variable rate input and to the FSM, wherein the variable rate symbol mapper, for each symbol period, receives the at least one input bit, the FSM output bit, and a mode selection input that selects a constellation of a plurality of supported constellations including a Quadrature Phase Shift Keying (QPSK) constellation and at least one higher order constellation;
• wherein at least the FSM output bit is employed to indicate a plurality of valid constellation points of a selected constellation, wherein the plurality of valid constellation points is a subset of all constellation points of the selected constellation;
• and
• wherein:
• the FSM includes a plurality of storage elements and a plurality of modulo-two adders that are intercoupled with one another;
• the FSM is characterized by a parity check matrix having a set of elements, wherein each element of the set of elements corresponds to a particular coded bit of the set of coded bits;
• and
• an element of the set of elements of the parity check matrix corresponding to the FSM output bit includes a plurality of constituent components, wherein at least one constituent component of the plurality of constituent components is identical to an element of the parity check matrix corresponding to a coded bit of the set of coded bits other than the FSM output bit.

A variable data rate Trellis Code Modulation (TCM) encoder comprising:

• a variable rate input that receives at least one input bit each symbol period;
• a Finite State Machine (FSM) receiving two FSM inputs, wherein a first FSM input of the two FSM inputs receives a first input bit of the at least one input but, wherein a second FSM input of the two FSM inputs receives a second input bit of the at least one input bit when present and receives a zero when the second input bit of the at least one input bit is not present, wherein each symbol period the FSM produces an FSM output bit based upon the two FSM inputs;
• a variable rate symbol mapper operably coupled to the variable rate input and to the FSM, wherein the variable rate symbol mapper, for each symbol period, receives the at least one input bit, the FSM output bit, and a mode selection input that selects a constellation of a plurality of supported constellations including a Quadrature Phase Shift Keying (QPSK) constellation and at least one higher order constellation;
• wherein at least the FSM output bit is employed to indicate a plurality of valid constellation points of a selected constellation, wherein the plurality of valid constellation points is a subset of all constellation points of the selected constellation;
• and
• wherein:
• the FSM includes four storage elements;
• and
• the FSM is characterized by a parity check matrix having a set of elements, wherein each element of the set of elements corresponds to a particular coded bit of the set of coded bits and the parity check matrix is:
• [D3+D2+D, D2, D4+D+1] or the time-reversed equivalent thereof.

A wireless communication device comprising:

• a Radio Frequency (RF) transceiver;
• a baseband receiver section operably coupled to the RF transceiver;
• and
• a baseband transmitter section operably coupled to the RF transceiver that includes a variable data rate Trellis Code Modulation (TCM) encoder having:
• a variable rate input that receives at least one input bit each symbol period;
• a Finite State Machine (FSM) receiving two FSM inputs, wherein a first FSM input of the two FSM inputs receives a first input bit of the at least one input but, wherein a second FSM input of the two FSM inputs receives a second input bit of the at least one input bit when present and receives a zero when the second input bit of the at least one input bit is not present, wherein each symbol period the FSM produces an FSM output bit based upon the two FSM inputs;
• a variable rate symbol mapper operably coupled to the variable rate input and to the FSM, wherein the variable rate symbol mapper, for each symbol period, receives the at least one input bit, the FSM output bit, and a mode selection input that selects a constellation of a plurality of supported constellations including a Quadrature Phase Shift Keying (QPSK) constellation and at least one higher order constellation;
• wherein at least the FSM output bit is employed to indicate a plurality of valid constellation points of a selected constellation, wherein the plurality of valid constellation points is a subset of all constellation points of the selected constellation;
• and
• wherein the variable data rate TCM encoder produces TCM codes with optimal Euclidean distance properties for the QPSK constellation and near optimal Euclidian distance properties for the at least one higher order constellation.

A method for Trellis Code Modulating at least one input bit, the method comprising:

• receiving at least one input bit each symbol period;
• encoding, with a Finite State Machine (FSM) each symbol period, a first FSM input and a second FSM input to produce an FSM output bit, wherein the FSM input receives a first input bit of the at least one input but, wherein the second FSM input receives a second input bit of the at least one input bit when present and receives a zero when the second input bit of the at least one input bit is not present;
• selecting, each symbol period, a constellation of a plurality of supported constellations including a Quadrature Phase Shift Keying (QPSK) constellation and at least one higher order constellation;
• using at least the FSM output bit to indicate a plurality of valid constellation points of a selected constellation, wherein the plurality of valid constellation points is a subset of all constellation points of the selected constellation;
• using at least a first input bit of the at least one input bit to select a constellation point of the plurality of valid constellation points as a variable data rate Trellis Code Modulated output;
• and
• wherein codes produced have optimal Euclidean distance properties for the QPSK constellation and near optimal Euclidian distance properties for the at least one higher order constellation.