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

1. 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 bit, 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, wherein:

the FSM includes three storage elements and two modulo-two adders that are inter-coupled with one another; and

the FSM is characterized by a parity check matrix of [D 2 , D, D 3 +D 2 +1] or the time-reversed equivalent thereof;

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.

2. The variable data rate TCM of claim 1 , wherein when the mode selection input selects a QPSK constellation:

the at least one input bit includes only a first input bit;

the second FSM input is zero; and

the FSM output bit indicates a pair of valid constellation points for the QPSK constellation.

3. The variable data rate TCM of claim 2 , wherein when die mode selection input selects an 8-Quadrature Amplitude Modulated (QAM) constellation of the at least one higher order constellation:

the at least one input bit includes a first input bit and a second input bit; and

the FSM output bit and the first input bit indicate a set of valid constellation points for the 8-QAM constellation.

4. The variable data rate TCM of claim 2 , wherein when the mode selection input selects a 16-Quadrature Amplitude Modulated (QAM) constellation of the at least one higher order constellation:

the at least one input bit includes a first input bit, a second input bit, and a third input bit; and

the FSM output bit, the first input bit, and the second input bit indicate a set of valid constellation points for the 16-QAM constellation.

5. The variable data rate TCM of claim 2 , wherein when the mode selection input selects a 32-Quadrature Amplitude Modulated (QAM) constellation of the at least one higher order constellation:

the at least one input bit includes a first input bit, a second input bit, a third input bit, and a fourth input bit; and

the FSM output bit, the first input bit, and the second input bit indicate a set of valid constellation points for the 32-QAM constellation.

6. Thy variable data rate TCM of claim 2 , wherein when the mode selection input selects a 64-Quadrature Amplitude Modulated (QAM) constellation of the at least one higher order constellation:

the at least one input bit includes a first input bit, a second input bit, a third input bit, a fourth input bit, and a fifth input, bit; and

the FSM output bit, the first input bit, and the second input bit indicate a set of valid constellation points for the 64-QAM constellation.

7. The variable data rate TCM of claim 1 , wherein the variable data rate TCM output is two-dimensional.

8. The variable data rate TCM of claim 1 , wherein:

the Euclidean distance properties for the QPSK constellation is 6d 2 where d is the distance between constellation points; and

the Euclidian distance properties for the at least one higher order constellation is 5d 2 .

9. 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 bit 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, wherein:

the FSM includes three storage elements and two modulo-two adders that are inter-coupled with one another; and

the FSM is characterized by a party check matrix of [D 2 , D, D 3 +D 2 +1] or the time-reversed equivalent thereof;

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 paints 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 new optimal Euclidian distance properties for the at least one higher order constellation.

10. The variable data rate TCM of claim 9 , wherein when the mode selection input selects an 8-Quadrature Amplitude Modulated (QAM) constellation of the at least one higher order constellation:

the at least one input bit includes a first input bit and a second input bit; and

the FSM output bit and the first input bit indicate a set of valid constellation points for the 8-QAM constellation.

11. The variable data rate TCM of claim 9 , wherein when the mode selection input selects a 16-Quadrature Amplitude Modulated (QAM) constellation of the at least one higher order constellation:

the at least one input bit includes a first input bit, a second input bit, and a third input bit; and

the FSM output bit the first input bit, and the second input bit indicate a set of valid constellation points for the 16-QAM constellation.

12. The variable data rate TCM of claim 9 , wherein when the mode selection input selects a 32-Quadrature Amplitude Modulated (QAM) constellation of the at least one higher order constellation:

the at least one input bit includes a first input hit, s second input bit a third input bit, and a fourth input bit; and

the FSM output bit, the first input bit, and the second input bit indicate a set of valid constellation points for the 32-QAM constellation.

13. The variable data rate TCM of claim 9 , wherein when the mode selection input selects a 64-Quadrature Amplitude Modulated (QAM) constellation of the at least one higher order constellation:

the at least one input bit includes a first input bit, a second input bit, a third input bit, a fourth input bit, And a fifth input bit; and

the FSM output bit the first input bit, and the second input bit indicate a set of valid constellation points fir the 64-QAM constellation.

14. 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 bit, 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) constipation 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 three storage elements and two modulo-two adders that are inter-coupled with one another,

the FSM is characterized by a parity check matrix of [D 2 , D, D 3 +D 2 +1] or the time-reversed equivalent thereof element of the set; 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.

15. The variable data rate TCM of claim 14 , wherein:

the Euclidean distance properties for the QPSK constellation is 6d 2 where d is the distance between constellation points; and

the Euclidian distance properties for the at least one higher order constellation is 5d 2 .

16. 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 bit, 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: [D 3 +D 2 +D, D 2 , D 4 +1] or the time-reversed equivalent thereof.

17. The variable data rate TCM of claim 16 , wherein:

the Euclidean distance properties for the QPSK constellation as 7d 2 where d is the distance between constellation points; and

the Euclidian distance properties for the at least one higher order constellation is 6d 2 .

18. 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 bit 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, wherein:

the FSM includes three storage elements and two modulo-two adders that are inter-coupled with one another; and

the FSM is characterized by a parity check matrix of [D 2 , D, D 3 +D 2 +1] or the time-reversed equivalent thereof;

a variable rate symbol mapper operably coupled to the variable rate input and to the FSM, wherein the variable rate symbol mapper, far 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.

19. The wireless communication device of claim 18 , wherein:

the Euclidean distance properties for the QPSK constellation is 6d 2 where d is the distance between constellation points; and

the Euclidian distance properties for the at least one higher order constellation is 5d 2 .

20. The wireless communication device of claim 18 , wherein the receiver section further comprises:

a decision feedback equalizer that equalizes incoming signals and produces a plurality of soft decision corresponding to each symbol of a plurality of received symbols; and

a variable TCM decoder that receives the plurality of soft decisions and performs TCM decoding operations consistent with the variable data rate TCM to produce output data.

21. The wireless communication device if claim 20 , wherein the TCM decoder of the receiver section further comprises a FSM tat corresponds to the FSM of the TCM of transmitter section.

22. A method for Trellis Code Modulating at least one input bit, the medium 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 bit, 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, wherein:

the FSM is operable to implement an inter-coupled combination of three storage elements and two modulo-two adders; and

the FSM is operable to implement a parity check matrix of [D 2 , D, D 3 +D 2 +1] or the time-reversed equivalent thereof;

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.

23. The method of claim 22 , wherein when the QPSK constellation is selected:

the at least one input bit includes only a first input bit;

the second FSM input is zero; and

the FSM output bit indicates a pair of valid constellation points for the QPSK constellation.

24. The method of claim 23 , wherein when an 8-Quadrature Amplitude Modulated (QAM) constellation of the at least one higher order constellation is selected:

the at least one input bit includes a first input bit and a second input bit; and

the FSM output bit and the first input bit indicate a set of valid constellation points for the 8-QAM constellation.

25. The method of claim 23 , wherein when a 16-Quadrature Amplitude Modulated (QAM) constellation of the at least one higher order constellation is selected:

the FSM output bit, the first input bit, and the second input bit indicate a set of valid constellation points for the 16-QAM constellation; and

a third input bit of the at least one input bit selects a constellation point of the set of valid constellation points as the variable data rate TCM output.

26. The method of claim 23 , wherein when a 32-Quadrature Amplitude Modulated (QAM) constellation of the at least one higher order constellation is selected:

the at least one input bit includes a first input bit, a second input bit, a third input bit, and a fourth input bit; and

the FSM output bit, the first input bit, and the second input bit indicate a set of valid constellation points for the 32-QAM constellation.

27. The method of claim 23 , wherein when a 64-Quadrature Amplitude Modulated (QAM) constellation of the at least one higher order constellation is selected the at least one input bit includes a first input bit, a second input bit, a third input bit a fourth input bit, and a fifth input bit; and

the FSM output bit, the first input bit, and the second input bit indicate a set of valid constellation points for the 64-QAM constellation.

28. The method of claim 22 , wherein the variable data rate Trellis Code Modulated output is two-dimensional.