Methods and apparatuses for signaling with geometric constellations in a Raleigh fading channel
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. 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 d min , 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.
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;
a mapper configured to map encoded bits to symbols in a symbol constellation;
a modulator configured to generate a signal for transmission via the communication channel using symbols generated by the mapper;
wherein the receiver, comprises:
a demodulator configured to demodulate the received signal via the communication channel;
a demapper configured to estimate likelihoods from the demodulated signal;
a decoder that is configured to estimate decoded bits from the likelihoods generated by the demapper; and
wherein the points of the symbol, constellation have non-uniform inter-point distances selected to achieve a gain in capacity for a predetermined signal to noise ratio (SNR) relative to a symbol, constellation having uniform inter-point distances: and
wherein the constellation provides an increase in capacity at a predetermined SNR that is at least 5% of the gain in capacity achieved by a constellation optimized for at least one of joint capacity and parallel decode PD capacity at the predetermined SNR in a Raleigh fading channel.
2. The communication system of claim 1 , wherein the code is a Turbo code.
3. The communication system of claim 1 , wherein the code is a LDPC code.
4. The communication system of claim 1 , wherein the constellation provides an increase in capacity at a predetermined SNR that is at least 20% of the gain in capacity achieved by a constellation optimized for joint capacity at the predetermined SNR in a Raleigh fading channel.
5. The communication system of claim 1 , wherein the constellation provides an increase in capacity at a predetermined SNR that is at least 50% of the gain in capacity achieved by a constellation optimized for joint capacity at the predetermined SNR in a Raleigh fading channel.
6. The communication system of claim 1 , wherein the constellation provides an increase in capacity at a predetermined SNR that is at least 90% of the gain in capacity achieved by a constellation optimized for joint capacity at the predetermined SNR in a Raleigh fading channel.
7. The communication system of claim 1 , wherein the constellation provides an increase in capacity at a predetermined SNR that is at least 100% of the gain in capacity achieved by a constellation optimized for joint capacity at the predetermined SNR in a Raleigh fading channel.
8. The communication system of claim 1 , wherein the constellation provides an increase in capacity at a predetermined SNR that is at least 20% of the gain in capacity achieved by a constellation optimized for PD capacity at the predetermined SNR in a Raleigh fading channel.
9. The communication system of claim 1 , wherein the constellation provides an increase in capacity at a predetermined SNR that is at least 50% of the gain in capacity achieved by a constellation optimized for PD capacity at the predetermined SNR in a Raleigh fading channel.
10. The communication system of claim 1 , wherein the constellation provides an increase in capacity at a predetermined SNR that is at least 70% of the gain in capacity achieved by a constellation optimized for PD capacity at the predetermined SNR in a Raleigh fading channel.
11. The communication system of claim 1 , wherein the constellation provides an increase in capacity at a predetermined SNR that is at least 90% of the gain in capacity achieved by a constellation optimized for PD capacity at the predetermined SNR in a Raleigh fading channel.
12. The communication system of claim 1 , wherein the constellation provides an increase in capacity at a predetermined SNR that is at least 100% of the gain in capacity achieved by a constellation optimized for PD capacity at the predetermined SNR in a Raleigh fading channel.
13. The communication system of claim 1 , wherein the symbol constellation is a PAM-8 symbol constellation having constellation points within at least one of the ranges specified in FIGS. 25-47 .
14. The communication system of claim 1 , wherein the symbol constellation is a PAM-16 symbol constellation having constellation points within at least one of the ranges specified in FIGS. 48-71 .
15. The communication system of claim 1 , wherein the symbol constellation is a PAM-32 symbol constellation having constellation points within at least one of the ranges specified in FIGS. 72-95 .
16. The communication system of claim 1 , wherein the symbol constellation is a N-Dimensional symbol constellation, where the constellation points in at least one dimension are within at least one of the ranges specified in FIGS. 25-95 .