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摘要

Communication systems are described that use signal constellations, which have unequally spaced (i.e. ‘geometrically’ shaped) points. In many embodiments, the communication systems use specific geometric constellations that are capacity optimized at a specific SNR, over the Rayleigh fading channel. In addition, ranges within which the constellation points of a capacity optimized constellation can be perturbed and are still likely to achieve a given percentage of the optimal capacity increase compared to a constellation that maximizes dmin, are also described. Capacity measures that are used in the selection of the location of constellation points include, but are not limited to, parallel decode (PD) capacity and joint capacity.

說(shuō)明書(shū)

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CROSS-REFERENCE TO RELATED APPLICATIONS

權(quán)利要求

1

What is claimed is:

1. A communication system, comprising:a transmitter capable of transmitting signals via a communication channel;

wherein the transmitter comprises:a coder capable of receiving bits and outputting encoded bits using a Low Density Parity Check (LDPC) code;

a mapper, coupled to the coder, capable of mapping encoded bits to symbols in a non-uniform quadrature amplitude modulation 1024-point symbol constellation (NU-QAM 1024);

a modulator, coupled to the mapper, capable of producing a signal for transmission via the communication channel based upon symbols generated by the mapper;

a receiver capable of receiving signals via the communication channel at a channel signal-to-noise ratio (SNR), wherein the receiver comprises:

a demodulator capable of demodulating a received signal into a demodulated signal;

a demapper, coupled to the demodulator, capable of determining likelihoods using the NU-QAM 1024; and

a decoder, coupled to the demapper, capable of using likelihoods determined by the demapper to provide a sequence of received bits based upon the LDPC code;

wherein the NU-QAM 1024 comprises an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.7560 from the following set of amplitudes:

?38.3887, ?32.0467, ?27.2059, ?24.0230, ?20.1597, ?18.7135, ?15.4053, ?15.0236, ?11.086, ?11.0231, ?8.0271, ?8.0244, ?4.4028, ?4.4028, ?1.8543, ?1.8540, 1.8561, 1.8565, 4.4049, 4.4049, 8.0268, 8.0295, 11.0254, 11.0873, 15.026, 15.4055, 18.7141, 20.1578, 24.0205, 27.2021, 32.0412, 38.3824.

2. The communication system of claim 1, wherein each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.31 from the following set of amplitudes:?38.3887, ?32.0467, ?27.2059, ?24.0230, ?20.1597, ?18.7135, ?15.4053, ?15.0236, ?11.086, ?11.0231, ?8.0271, ?8.0244, ?4.4028, ?4.4028, ?1.8543, ?1.8540, 1.8561, 1.8565, 4.4049, 4.4049, 8.0268, 8.0295, 11.0254, 11.0873, 15.026, 15.4055, 18.7141, 20.1578, 24.0205, 27.2021, 32.0412, 38.3824.

3. The communication system of claim 1, wherein each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are:?38.3887, ?32.0467, ?27.2059, ?24.0230, ?20.1597, ?18.7135, ?15.4053, ?15.0236, ?11.086, ?11.0231, ?8.0271, ?8.0244, ?4.4028, ?4.4028, ?1.8543, ?1.8540, 1.8561, 1.8565, 4.4049, 4.4049, 8.0268, 8.0295, 11.0254, 11.0873, 15.026, 15.4055, 18.7141, 20.1578, 24.0205, 27.2021, 32.0412, 38.3824.

4. The communication system of claim 1, wherein the transmitter is capable of selecting the NU-QAM 1024 constellation from a plurality of constellations including a plurality of symbol constellations.

5. The communication system of claim 1, wherein the transmitter is capable of selecting an LDPC code rate and the NU-QAM 1024 constellation from a plurality of symbol constellations as a pair from a plurality of predetermined LDPC code rate and non-uniform constellation pairs.

6. The communication system of claim 1, wherein the symbols in the NU-QAM 1024 are labelled using gray labels.

7. The communication system of claim 1, wherein the symbols in the NU-QAM 1024 are labelled using binary reflective gray labels.

8. The digital communication system of claim 1, wherein the LDPC code has a code rate that is equal to or less than 0.56526.

9. The digital communication system of claim 4, wherein the NU-QAM 1024 constellation is characterized in that the NU-QAM 1024 constellation provides greater parallel decode capacity at a specific signal-to-noise ratio (SNR) compared to a QAM 1024 constellation that maximizes d_minat the specific SNR.

10. The digital communication system of claim 4, wherein the NU-QAM 1024 constellation is characterized in that selection of the NU-QAM 1024 constellation from the plurality of symbol constellations in combination with an LDPC code rate that is equal to or less than 0.56526 enables a receiver to decode the transmitted signals when the communication channel has a signal-to-noise ratio (SNR) at the receiver that is between 20.0 dB and 20.8 dB.

11. The digital communication system of claim 4, wherein the NU-QAM 1024 constellation is characterized in that selection of the NU-QAM 1024 constellation from the plurality of symbol constellations enables a receiver to decode the transmitted signals when the communication channel has a signal-to-noise ratio (SNR) at the receiver that is between 18.8 dB and 20.8 dB.

12. The digital communication system of claim 4, wherein the NU-QAM 1024 constellation is characterized in that selection of the NU-QAM 1024 constellation from the plurality of symbol constellations enables a receiver to decode the transmitted signals when the communication channel has a signal-to-noise ratio (SNR) at the receiver of 18.8 dB.

13. The digital communication system of claim 4, wherein the transmitter is configured to select the NU-QAM 1024 constellation in combination with an LDPC code rate that is equal to or less than 0.56526.

14. The communication system of claim 5, wherein:the transmitter is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a second LDPC code rate and NU-QAM pair having a code rate less than or equal to or less than 0.27212 and a second NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.6870 from the following set of amplitudes:

?37.9896, ?30,4644, ?26.1314, ?25.8467, ?18.8919, ?18.8919, ?18.1165, ?17.8829, ?8.2966, ?8.2966, ?8.2966, ?8.2966, ?4.9384, ?4.9384, ?4.9004, ?4.8867, 4.8863, 4.9008, 4.9384, 4.9384, 8.2966, 8.2966, 8.2966, 8.2966, 17.8840, 18.1156, 18.8918, 18.8918, 25.8467, 25.8467, 26.1314, 30.4644, and 37.9896.

15. The communication system of claim 5, wherein:the transmitter is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a third LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.34894 and a third NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.602 from the following set of amplitudes:

?38.8088, ?31.7370, ?26.1892, ?25.0630, ?18.4668, ?18.4668, ?16.6894, ?16.6675, ?9.2115, ?9.2115, ?9.0888, ?9.0480, ?3.7549, ?3.7549, ?3.7549, ?3.7549, 3.7539, 3.7539, 3.7539, 3.7539, 9.0476, 9.0509, 9.2107, 9.2107, 16.6677, 16.6875, 18.4662, 18.4662, 25.0617, 26.1893, 31.7383, and 38.8190.

16. The communication system of claim 5, wherein:the transmitter is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a fourth LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.40756 and a fourth NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.5190 from the following set of amplitudes:

?39.2317, ?32.0637, ?26.2140, ?24.6366, ?18.7399, ?18.5633, ?15.9554, ?15.9554, ?9.5560, ?9.5560, ?8.9852, ?8.9797, ?3.3963, ?3.3963, ?3.3645, ?3.3634, 3.3646, 3.3653, 3.3966, 3.3966, 8.9803, 8.9851, 9.5562, 9.5562, 15.9543, 15.9543, 18.5618, 18.7381, 24.6352, 26.2126, 32.0635, and 39.2363.

17. The communication system of claim 5, wherein:the transmitter is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a fifth LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.54052 and a fifth NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.3410 from the following set of amplitudes:

?38.5955, ?32.0616, ?27.0615, ?24.0453, ?19.9129, ?18.8201, ?15.3494, ?15.1509, ?10.9280, ?10.9088, ?8.0512, ?8.0512, ?4.2608, ?4.2608, ?1.9778, ?1.9769, 1.9789, 1.9801, 4.2617, 4.2617, 8.0509, 8.0509, 10.9084, 10.9264, 15.1515, 15.3492, 18.8213, 19.9127, 24.0456, 27.0586, 32.0594, 38.5954.

18. The communication system of claim 5, wherein:the transmitter is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a seventh LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.6387 and a seventh NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.254 from the following set of amplitudes:

?37.7602, ?32.0093, ?27.5785, ?24.2219, ?20.9075, ?18.6078, ?15.8834, ?14.4076, ?11.4808, ?10.7002, ?7.9842, ?7.6972, ?4.5506, ?4.4707, ?1.6645, ?1.6412, 1.6435, 1.6666, 4.4731, 4.5532, 7.7004, 7.9858, 10.7014, 11.4808, 14.4074, 15.8829, 18.6066, 20.9060, 24.2204, 27.5770, 32.0068, and 37.7537.

19. The communication system of claim 5, wherein:the transmitter is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is an eighth LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.69882 and an eighth NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.441 from the following set of amplitudes:

?36.8223, ?31.6346, ?27.5952, ?24.3912, ?21.3627, ?18.9630, ?16.4909, ?14.6073, ?12.2395, ?10.7040, ?8.5985, ?7.3701, ?5.1427, ?4.1180, ?2.0669, ?1.1401, 1.1397, 2.0664, 4.1177, 5.1424, 7.3697, 8.5984, 10.7038, 12.2394, 14.6073, 16.4909, 18.9632, 21.3631, 24.3917, 27.5958, 31.6352, and 36.8223.

20. The communication system of claim 5, wherein:the transmitter is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a ninth LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.76978 and a ninth NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.2830 from the following set of amplitudes:

?35.7806, ?31.1542, ?27.5041, ?24.5029, ?21.7164, ?19.3443, ?17.0214, ?15.0190, ?12.8993, ?11.1053, ?9.1812, ?7.5809, ?5.6791, ?4.1763, ?2.3910, ?0.9323, 0.9322, 2.3910, 4.1762, 5.6791, 7.5809, 9.1813, 11.1053, 12.8772, 15.0190, 17.0214, 19.3443, 21.7164, 24.5029, 27.5041, 31.1543, and 35.7805.

21. The communication system of claim 5, wherein:the transmitter is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a tenth LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.86236 and a tenth NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.185 from the following set of amplitudes:

?34.7205, ?30.6582, ?27.3954, ?24.6158, ?22.0414, ?19.7371, ?17.5199, ?15.4780, ?13.4322, ?11.5522, ?9.6593, ?7.8881, ?6.0512, ?4.3433, ?2.5729, ?0.8935, 0.8940, 2.5734, 4.3438, 6.0516, 7.8885, 9.6597, 11.5525, 13.4325, 15.4781, 17.5200, 19.7371, 22.0413, 24.6154, 27.3948, 30.6573, and 34.7190.

22. The communication system of claim 4, wherein the plurality of symbol constellations includes multiple different sixty-four-point non-uniform symbol constellations, multiple different two-hundred-fifty-six-point non-uniform symbol constellations, and multiple different one-thousand-twenty-four-point non-uniform symbol constellations.

23. A communication system, comprising:a transmitter capable of transmitting signals via a communication channel;

wherein the transmitter comprises:a coder capable of receiving bits and outputting encoded bits using a Low Density Parity Check (LDPC) code;

a mapper, coupled to the coder, capable of mapping encoded bits to symbols in a non-uniform quadrature amplitude modulation 1024-point symbol constellation (NU-QAM 1024); and

a modulator, coupled to the mapper, capable of producing a signal for transmission via the communication channel based upon symbols generated by the mapper;

wherein the NU-QAM 1024 comprises an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.756 from the following set of amplitudes:

?38.3887, ?32.0467, ?27.2059, ?24.0230, ?20.1597, ?18.7135, ?15.4053, ?15.0236, ?11.086, ?11.0231, ?8.0271, ?8.0244, ?4.4028, ?4.4028, ?1.8543, ?1.8540, 1.8561, 1.8565, 4.4049, 4.4049, 8.0268, 8.0295, 11.0254, 11.0873, 15.026, 15.4055, 18.7141, 20.1578, 24.0205, 27.2021, 32.0412, 38.3824.

24. The communication system of claim 23, wherein each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.31 from the following set of amplitudes:?38.3887, ?32.0467, ?27.2059, ?24.0230, ?20.1597, ?18.7135, ?15.4053, ?15.0236, ?11.086, ?11.0231, ?8.0271, ?8.0244, ?4.4028, ?4.4028, ?1.8543, ?1.8540, 1.8561, 1.8565, 4.4049, 4.4049, 8.0268, 8.0295, 11.0254, 11.0873, 15.026, 15.4055, 18.7141, 20.1578, 24.0205, 27.2021, 32.0412, 38.3824.

25. The communication system of claim 23, wherein each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are:?38.3887, ?32.0467, ?27.2059, ?24.0230, ?20.1597, ?18.7135, ?15.4053, ?15.0236, ?11.086, ?11.0231, ?8.0271, ?8.0244, ?4.4028, ?4.4028, ?1.8543, ?1.8540, 1.8561, 1.8565, 4.4049, 4.4049, 8.0268, 8.0295, 11.0254, 11.0873, 15.026, 15.4055, 18.7141, 20.1578, 24.0205, 27.2021, 32.0412, 38.3824.

26. The communication system of claim 23, wherein the transmitter is capable of selecting the NU-QAM 1024 constellation from a plurality of constellations including a plurality of symbol constellations.

27. The communication system of claim 23, wherein the transmitter is capable of selecting an LDPC code rate and the NU-QAM 1024 constellation from a plurality of symbol constellations as a pair from a plurality of predetermined LDPC code rate and non-uniform constellation pairs.

28. The communication system of claim 23, wherein the symbols in the (NU-QAM 1024 are labelled using gray labels.

29. The communication system of claim 23, wherein the symbols in the NU-QAM 1024 are labelled using binary reflective gray labels.

30. The digital communication system of claim 23, wherein the LDPC code has a code rate that is equal to or less than 0.56526.

31. The digital communication system of claim 26, wherein the NU-QAM 1024 constellation is characterized in that the NU-QAM 1024 constellation provides greater parallel decode capacity at a specific signal-to-noise ratio (SNR) compared to a QAM 1024 constellation that maximizes d_minat the specific SNR.

32. The digital communication system of claim 26, wherein the NU-QAM 1024 constellation is characterized in that selection of the NU-QAM 1024 constellation from the plurality of symbol constellations in combination with an LDPC code rate that is equal to or less than 0.56526 enables a receiver to decode the transmitted signals when the communication channel has a signal-to-noise ratio (SNR) at the receiver that is between 20.0 dB and 20.8 dB.

33. The digital communication system of claim 26, wherein the NU-QAM 1024 constellation is characterized in that selection of the NU-QAM 1024 constellation from the plurality of symbol constellations enables a receiver to decode the transmitted signals when the communication channel has a signal-to-noise ratio (SNR) at the receiver that is between 18.8 dB and 20.8 dB.

34. The digital communication system of claim 26, wherein the NU-QAM 1024 constellation is characterized in that selection of the NU-QAM 1024 constellation from the plurality of symbol constellations enables a receiver to decode the transmitted signals when the communication channel has a signal-to-noise ratio (SNR) at the receiver of 18.8 dB.

35. The digital communication system of claim 26, wherein the transmitter is configured to select the NU-QAM 1024 constellation in combination with an LDPC code rate that is equal to or less than 0.56526.

36. The communication system of claim 27, wherein:the transmitter is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a second LDPC code rate and NU-QAM pair having a code rate less than or equal to or less than 0.27212 and a second NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.6870 from the following set of amplitudes:

?37.9896, ?30,4644, ?26.1314, ?25.8467, ?18.8919, ?18.8919, ?18.1165, ?17.8829, ?8.2966, ?8.2966, ?8.2966, ?8.2966, ?4.9384, ?4.9384, ?4.9004, ?4.8867, 4.8863, 4.9008, 4.9384, 4.9384, 8.2966, 8.2966, 8.2966, 8.2966, 17.8840, 18.1156, 18.8918, 18.8918, 25.8467, 25.8467, 26.1314, 30.4644, and 37.9896.

37. The communication system of claim 27, wherein:the transmitter is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a third LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.34894 and a third NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.602 from the following set of amplitudes:

?38.8088, ?31.7370, ?26.1892, ?25.0630, ?18.4668, ?18.4668, ?16.6894, ?16.6675, ?9.2115, ?9.2115, ?9.0888, ?9.0480, ?3.7549, ?3.7549, ?3.7549, ?3.7549, 3.7539, 3.7539, 3.7539, 3.7539, 9.0476, 9.0509, 9.2107, 9.2107, 16.6677, 16.6875, 18.4662, 18.4662, 25.0617, 26.1893, 31.7383, and 38.8190.

38. The communication system of claim 27, wherein:the transmitter is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a fourth LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.40756 and a fourth NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.5190 from the following set of amplitudes:

?39.2317, ?32.0637, ?26.2140, ?24.6366, ?18.7399, ?18.5633, ?15.9554, ?15.9554, ?9.5560, ?9.5560, ?8.9852, ?8.9797, ?3.3963, ?3.3963, ?3.3645, ?3.3634, 3.3646, 3.3653, 3.3966, 3.3966, 8.9803, 8.9851, 9.5562, 9.5562, 15.9543, 15.9543, 18.5618, 18.7381, 24.6352, 26.2126, 32.0635, and 39.2363.

39. The communication system of claim 27, wherein:the transmitter is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a fifth LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.54052 and a fifth NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.3410 from the following set of amplitudes:

?38.5955, ?32.0616, ?27.0615, ?24.0453, ?19.9129, ?18.8201, ?15.3494, ?15.1509, ?10.9280, ?10.9088, ?8.0512, ?8.0512, ?4.2608, ?4.2608, ?1.9778, ?1.9769, 1.9789, 1.9801, 4.2617, 4.2617, 8.0509, 8.0509, 10.9084, 10.9264, 15.1515, 15.3492, 18.8213, 19.9127, 24.0456, 27.0586, 32.0594, 38.5954.

40. The communication system of claim 27, wherein:the transmitter is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a seventh LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.6387 and a seventh NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.254 from the following set of amplitudes:

?37.7602, ?32.0093, ?27.5785, ?24.2219, ?20.9075, ?18.6078, ?15.8834, ?14.4076, ?11.4808, ?10.7002, ?7.9842, ?7.6972, ?4.5506, ?4.4707, ?1.6645, ?1.6412, 1.6435, 1.6666, 4.4731, 4.5532, 7.7004, 7.9858, 10.7014, 11.4808, 14.4074, 15.8829, 18.6066, 20.9060, 24.2204, 27.5770, 32.0068, and 37.7537.

41. The communication system of claim 27, wherein:the transmitter is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is an eighth LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.69882 and an eighth NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.441 from the following set of amplitudes:

?36.8223, ?31.6346, ?27.5952, ?24.3912, ?21.3627, ?18.9630, ?16.4909, ?14.6073, ?12.2395, ?10.7040, ?8.5985, ?7.3701, ?5.1427, ?4.1180, ?2.0669, ?1.1401, 1.1397, 2.0664, 4.1177, 5.1424, 7.3697, 8.5984, 10.7038, 12.2394, 14.6073, 16.4909, 18.9632, 21.3631, 24.3917, 27.5958, 31.6352, and 36.8223.

42. The communication system of claim 27, wherein:the transmitter is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a ninth LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.76978 and a ninth NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.2830 from the following set of amplitudes:

?35.7806, ?31.1542, ?27.5041, ?24.5029, ?21.7164, ?19.3443, ?17.0214, ?15.0190, ?12.8993, ?11.1053, ?9.1812, ?7.5809, ?5.6791, ?4.1763, ?2.3910, ?0.9323, 0.9322, 2.3910, 4.1762, 5.6791, 7.5809, 9.1813, 11.1053, 12.8772, 15.0190, 17.0214, 19.3443, 21.7164, 24.5029, 27.5041, 31.1543, and 35.7805.

43. The communication system of claim 27, wherein:the transmitter is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a tenth LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.86236 and a tenth NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.185 from the following set of amplitudes:

?34.7205, ?30.6582, ?27.3954, ?24.6158, ?22.0414, ?19.7371, ?17.5199, ?15.4780, ?13.4322, ?11.5522, ?9.6593, ?7.8881, ?6.0512, ?4.3433, ?2.5729, ?0.8935, 0.8940, 2.5734, 4.3438, 6.0516, 7.8885, 9.6597, 11.5525, 13.4325, 15.4781, 17.5200, 19.7371, 22.0413, 24.6154, 27.3948, 30.6573, and 34.7190.

44. The communication system of claim 23, wherein the plurality of symbol constellations includes multiple different sixty-four-point non-uniform symbol constellations, multiple different two-hundred-fifty-six-point non-uniform symbol constellations, and multiple different one-thousand-twenty-four-point non-uniform symbol constellations.

45. A communication system, comprising:a receiver capable of receiving signals via a communication channel having a channel signal-to-noise ratio (SNR), wherein the receiver comprises:a demodulator capable of demodulating a received signal into a demodulated signal;

a demapper, coupled to the demodulator, capable of determining likelihoods using a non-uniform quadrature amplitude modulation 1024-point symbol constellation (NU-QAM 1024); and

a decoder, coupled to the demapper, capable of using likelihoods determined by the demapper to provide a sequence of received bits based upon the LDPC code; and

wherein the NU-QAM 1024 comprises an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.756 from the following set of amplitudes:

?38.3887, ?32.0467, ?27.2059, ?24.0230, ?20.1597, ?18.7135, ?15.4053, ?15.0236, ?11.086, ?11.0231, ?8.0271, ?8.0244, ?4.4028, ?4.4028, ?1.8543, ?1.8540, 1.8561, 1.8565, 4.4049, 4.4049, 8.0268, 8.0295, 11.0254, 11.0873, 15.026, 15.4055, 18.7141, 20.1578, 24.0205, 27.2021, 32.0412, 38.3824.

46. The communication system of claim 45, wherein each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.31 from the following set of amplitudes:?38.3887, ?32.0467, ?27.2059, ?24.0230, ?20.1597, ?18.7135, ?15.4053, ?15.0236, ?11.086, ?11.0231, ?8.0271, ?8.0244, ?4.4028, ?4.4028, ?1.8543, ?1.8540, 1.8561, 1.8565, 4.4049, 4.4049, 8.0268, 8.0295, 11.0254, 11.0873, 15.026, 15.4055, 18.7141, 20.1578, 24.0205, 27.2021, 32.0412, 38.3824.

47. The communication system of claim 45, wherein each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are:?38.3887, ?32.0467, ?27.2059, ?24.0230, ?20.1597, ?18.7135, ?15.4053, ?15.0236, ?11.086, ?11.0231, ?8.0271, ?8.0244, ?4.4028, ?4.4028, ?1.8543, ?1.8540, 1.8561, 1.8565, 4.4049, 4.4049, 8.0268, 8.0295, 11.0254, 11.0873, 15.026, 15.4055, 18.7141, 20.1578, 24.0205, 27.2021, 32.0412, 38.3824.

48. The digital communication system of claim 45, wherein the LDPC code rate has a code rate that is equal to or less than 0.56526.

49. The digital communication system of claim 45, wherein the receiver is configured to select the NU-QAM 1024 constellation from a plurality of symbol constellations.

50. The digital communication system of claim 49, wherein the NU-QAM 1024 constellation is characterized in that the NU-QAM 1024 constellation provides greater parallel decode capacity at a specific signal-to-noise ratio (SNR) compared to a QAM 1024 constellation that maximizes d_minat the specific SNR.

51. The digital communication system of claim 49, wherein the receiver is configured to select the NU-QAM 1024 constellation from the plurality of symbol constellations in combination with an LDPC code rate that is equal to or less than 0.56526 and the receiver is capable of decoding the signals received via the communication channel using the LDPC code rate and the NU-QAM 1024 symbol constellation when the communication channel SNR is between 20.0 dB and 20.8 dB.

52. The digital communication system of claim 49, wherein the receiver is capable of decoding the signals received via the communication channel using the NU-QAM 1024 constellation when the communication channel SNR is between 18.8 dB and 20.8 dB.

53. The digital communication system of claim 49, wherein the receiver is capable of decoding the signals received via the communication channel using the NU-QAM 1024 constellation when the communication channel SNR is 18.8 dB.

54. The digital communication system of claim 49, wherein the receiver is configured to select the NU-QAM 1024 constellation in combination with an LDPC code rate that is equal to or less than 0.56526.

55. The communication system of claim 49, wherein the receiver is capable of selecting an LDPC code rate and the NU-QAM 1024 symbol constellation from a plurality of symbol constellations as a pair from a plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs.

56. The communication system of claim 55, wherein each of the plurality of non-uniform symbol constellations is only included in one of the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs.

57. The communication system of claim 55, wherein:the receiver is configured to select an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a second LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.27212 and a second NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.6870 from the following set of amplitudes:

?37.9896, ?30,4644, ?26.1314, ?25.8467, ?18.8919, ?18.8919, ?18.1165, ?17.8829, ?8.2966, ?8.2966, ?8.2966, ?8.2966, ?4.9384, ?4.9384, ?4.9004, ?4.8867, 4.8863, 4.9008, 4.9384, 4.9384, 8.2966, 8.2966, 8.2966, 8.2966, 17.8840, 18.1156, 18.8918, 18.8918, 25.8467, 25.8467, 26.1314, 30.4644, and 37.9896.

58. The communication system of claim 55, wherein:the receiver is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a third LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.34894 and a third NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.602 from the following set of amplitudes:

?38.8088, ?31.7370, ?26.1892, ?25.0630, ?18.4668, ?18.4668, ?16.6894, ?16.6675, ?9.2115, ?9.2115, ?9.0888, ?9.0480, ?3.7549, ?3.7549, ?3.7549, ?3.7549, 3.7539, 3.7539, 3.7539, 3.7539, 9.0476, 9.0509, 9.2107, 9.2107, 16.6677, 16.6875, 18.4662, 18.4662, 25.0617, 26.1893, 31.7383, and 38.8190.

59. The communication system of claim 55, wherein:the receiver is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a fourth LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.40756 and a fourth NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.5190 from the following set of amplitudes:

?39.2317, ?32.0637, ?26.2140, ?24.6366, ?18.7399, ?18.5633, ?15.9554, ?15.9554, ?9.5560, ?9.5560, ?8.9852, ?8.9797, ?3.3963, ?3.3963, ?3.3645, ?3.3634, 3.3646, 3.3653, 3.3966, 3.3966, 8.9803, 8.9851, 9.5562, 9.5562, 15.9543, 15.9543, 18.5618, 18.7381, 24.6352, 26.2126, 32.0635, and 39.2363.

60. The communication system of claim 55, wherein:the receiver is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a fifth LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.54052 and a fifth NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.3410 from the following set of amplitudes:

?38.5955, ?32.0616, ?27.0615, ?24.0453, ?19.9129, ?18.8201, ?15.3494, ?15.1509, ?10.9280, ?10.9088, ?8.0512, ?8.0512, ?4.2608, ?4.2608, ?1.9778, ?1.9769, 1.9789, 1.9801, 4.2617, 4.2617, 8.0509, 8.0509, 10.9084, 10.9264, 15.1515, 15.3492, 18.8213, 19.9127, 24.0456, 27.0586, 32.0594, 38.5954.

61. The communication system of claim 55, wherein:the receiver is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a seventh LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.6387 and a seventh NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.254 from the following set of amplitudes:

?37.7602, ?32.0093, ?27.5785, ?24.2219, ?20.9075, ?18.6078, ?15.8834, ?14.4076, ?11.4808, ?10.7002, ?7.9842, ?7.6972, ?4.5506, ?4.4707, ?1.6645, ?1.6412, 1.6435, 1.6666, 4.4731, 4.5532, 7.7004, 7.9858, 10.7014, 11.4808, 14.4074, 15.8829, 18.6066, 20.9060, 24.2204, 27.5770, 32.0068, and 37.7537.

62. The communication system of claim 55, wherein:the receiver is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is an eighth LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.69882 and an eighth NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.441 from the following set of amplitudes:

?36.8223, ?31.6346, ?27.5952, ?24.3912, ?21.3627, ?18.9630, ?16.4909, ?14.6073, ?12.2395, ?10.7040, ?8.5985, ?7.3701, ?5.1427, ?4.1180, ?2.0669, ?1.1401, 1.1397, 2.0664, 4.1177, 5.1424, 7.3697, 8.5984, 10.7038, 12.2394, 14.6073, 16.4909, 18.9632, 21.3631, 24.3917, 27.5958, 31.6352, and 36.8223.

63. The communication system of claim 55, wherein:the receiver is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a ninth LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.76978 and a ninth NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.2830 from the following set of amplitudes:

?35.7806, ?31.1542, ?27.5041, ?24.5029, ?21.7164, ?19.3443, ?17.0214, ?15.0190, ?12.8993, ?11.1053, ?9.1812, ?7.5809, ?5.6791, ?4.1763, ?2.3910, ?0.9323, 0.9322, 2.3910, 4.1762, 5.6791, 7.5809, 9.1813, 11.1053, 12.8772, 15.0190, 17.0214, 19.3443, 21.7164, 24.5029, 27.5041, 31.1543, and 35.7805.

64. The communication system of claim 55, wherein:the receiver is capable of selecting an alternative LDPC code rate and NU-QAM 1024 symbol constellation pair from the plurality of predetermined LDPC code rate and non-uniform symbol constellation pairs, where the alternative LDPC code rate and NU-QAM 1024 symbol constellation pair is a tenth LDPC code rate and NU-QAM pair having a code rate equal to or less than 0.86236 and a tenth NU-QAM 1024 comprising an in-phase component and a quadrature component, where each component comprises 32 levels of amplitude such that the amplitudes scaled by a scaling factor are within 0.185 from the following set of amplitudes:

?34.7205, ?30.6582, ?27.3954, ?24.6158, ?22.0414, ?19.7371, ?17.5199, ?15.4780, ?13.4322, ?11.5522, ?9.6593, ?7.8881, ?6.0512, ?4.3433, ?2.5729, ?0.8935, 0.8940, 2.5734, 4.3438, 6.0516, 7.8885, 9.6597, 11.5525, 13.4325, 15.4781, 17.5200, 19.7371, 22.0413, 24.6154, 27.3948, 30.6573, and 34.7190.

65. The communication system of claim 45, wherein the plurality of symbol constellations includes multiple different sixty-four-point non-uniform symbol constellations, multiple different two-hundred-fifty-six-point non-uniform symbol constellations, and multiple different one-thousand-twenty-four-point non-uniform symbol constellations.

66. The digital communication system of claim 45, wherein the symbols in the NU-QAM 1024 are labelled using Gray labels.

67. The digital communication system of claim 45, wherein the symbols in the NU-QAM 1024 are labelled using binary reflective Gray labels.

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Methods and apparatuses for signaling with geometric constellations in a Rayleigh fading channel

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Methods and apparatuses for signaling with geometric constellations in a Rayleigh fading channel

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說(shuō)明書(shū)

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