Methodology and method and apparatus for signaling with capacity optimized constellations
Communication systems are described that use geometrically shaped constellations that have increased capacity compared to conventional constellations operating within a similar SNR band. In several embodiments, the geometrically shaped is optimized based upon a capacity measure such as parallel decoding capacity or joint capacity. In many embodiments, a capacity optimized geometrically shaped constellation can be used to replace a conventional constellation as part of a firmware upgrade to transmitters and receivers within a communication system. In a number of embodiments, the geometrically shaped constellation is optimized for an Additive White Gaussian Noise channel or a fading channel. In numerous embodiments, the communication uses adaptive rate encoding and the location of points within the geometrically shaped constellation changes as the code rate changes.
1. A digital communication system, comprising:
a transmitter configured to transmit signals to a receiver via a communication channel;
wherein the transmitter, comprises:
a coder configured to receive user bits and output encoded bits at an expanded output encoded bit rate using an LDPC code;
a mapper configured to map encoded bits to symbols in a QAM symbol constellation;
a modulator configured to generate a signal for transmission via the communication channel using symbols generated by the mapper; and
wherein the QAM symbol constellation is a geometrically spaced symbol constellation optimized for capacity using parallel decode capacity that provides a given capacity at a reduced signal-to-noise ratio compared to a QAM signal constellation that maximizes d min .
2. The communication system of claim 1 , wherein the geometrically spaced symbol constellation is capacity optimized subject to additional constraints.
3. The communication system of claim 1 , wherein the channel is an AWGN channel.
4. The communication system of claim 1 , wherein the channel is a fading channel.
5. The communication system of claim 1 , wherein the QAM constellation is a QAM-64 constellation.
6. The communication system of claim 5 , wherein the LDPC code is a rate 1/2 LDPC code.
7. The communication system of claim 6 , wherein the symbol constellation is formed using a PAM-8 constellation comprising the set of constellation points {−1.72, −0.81, 1.72, −0.62, 0.62, 0.02, 0.81, −0.02}.
8. The communication system of claim 5 , wherein the LDPC code is a rate 2/3 LDPC code.
9. The communication system of claim 8 , wherein the symbol constellation is formed using a PAM-8 constellation comprising the set of constellation points {−1.64, −0.97, 1.64, −0.58, 0.58, 0.15, 0.97, −0.15}.
10. The communication system of claim 5 , wherein the LDPC code is a rate 5/6 LDPC code.
11. The communication system of claim 10 , wherein the symbol constellation is formed using a PAM-8 constellation comprising the set of constellation points {−1.60, −1.03, −0.19, −0.58, 1.60, 1.03, 0.19, 0.58}.
12. The communication system of claim 1 , wherein the QAM constellation is a QAM-256 constellation.
13. The communication system of claim 12 , wherein the LDPC code is a rate 1/2 LDPC code.
14. The communication system of claim 13 , wherein the symbol constellation is formed using a PAM-16 constellation comprising the set of constellation points {−1.98, −1.29, 1.94, −1.17, −0.38, −0.65, −0.38, −0.68, 1.09, 0.76, 1.26, 0.76, 0.06, 0.29, 0.06, 0.29}.
15. The communication system of claim 12 , wherein the LDPC code is a rate 3/4 LDPC code.
16. The communication system of claim 15 , wherein the symbol constellation is formed using a PAM-16 constellation comprising the set of constellation points {−1.84, −1.42, 1.84, −1.11, −0.40, −0.65, −0.29, −0.83, 1.11, 0.84, 1.42, 0.65, 0.05, 0.29, −0.05, 0.40}.
17. A digital communication system, comprising:
a receiver configured to receive signals transmitted via a communication channel using a QAM symbol constellation;
wherein the receiver, comprises:
a demodulator configured to demodulate the signal received via the communication channel;
a demapper configured to estimate likelihoods of symbols in a QAM symbol constellation from the demodulated signal;
a decoder that is configured to estimate decoded bits from the likelihoods generated by the demapper using an LDPC code; and
wherein the QAM symbol constellation is a geometrically spaced symbol constellation optimized for capacity using parallel decode capacity that provides a given capacity at a reduced signal-to-noise ratio compared to a QAM signal constellation that maximizes d min .
18. The communication system of claim 17 , wherein the geometrically spaced symbol constellation is capacity optimized subject to additional constraints.
19. The communication system of claim 17 , wherein the channel is an AWGN channel.
20. The communication system of claim 17 , wherein the channel is a fading channel.
21. The communication system of claim 17 , wherein the QAM constellation is a QAM-64 constellation.
22. The communication system of claim 21 , wherein the LDPC code is a rate 1/2 LDPC code.
23. The communication system of claim 22 , wherein the symbol constellation is formed using a PAM-8 constellation comprising the set of constellation points {−1.72, −0.81, 1.72, −0.62, 0.62, 0.02, 0.81, −0.02}.
24. The communication system of claim 21 , wherein the LDPC code is a rate 2/3 LDPC code.
25. The communication system of claim 24 , wherein the symbol constellation is formed using a PAM-8 constellation comprising the set of constellation points {−1.64, −0.97, 1.64, −0.58, 0.58, 0.15, 0.97, −0.15}.
26. The communication system of claim 21 , wherein the LDPC code is a rate 5/6 LDPC code.
27. The communication system of claim 26 , wherein the symbol constellation is formed using a PAM-8 constellation comprising the set of constellation points {−1.60, −1.03, −0.19, −0.58, 1.60, 1.03, 0.19, 0.58}.
28. The communication system of claim 17 , wherein the QAM constellation is a QAM-256 constellation.
29. The communication system of claim 28 , wherein the LDPC code is a rate 1/2 LDPC code.
30. The communication system of claim 29 , wherein the symbol constellation is formed using a PAM-16 constellation comprising the set of constellation points {−1.98, −1.29, 1.94, −1.17, −0.38, −0.65, −0.38, −0.68, 1.09, 0.76, 1.26, 0.76, 0.06, 0.29, 0.06, 0.29}.
31. The communication system of claim 28 , wherein the LDPC code is a rate 3/4 LDPC code.
32. The communication system of claim 31 , wherein the symbol constellation is formed using a PAM-16 constellation comprising the set of constellation points {−1.84, −1.42, 1.84, −1.11, −0.40, −0.65, −0.29, −0.83, 1.11, 0.84, 1.42, 0.65, 0.05, 0.29, −0.05, 0.40}.