Constellation generation and re-evaluation

A method of operating a first modem operatively connected to a second modem through a communications system by generating a data constellation of data points for exchange of symbols between said first modem and said second modem, said method comprising:

• selecting a probability of error acceptable for communications between said first modem and said second modem;
• estimating a first minimum distance between adjacent symbols in the data constellation based upon said selected probability of error;
• calculating a first ratio of data constellation symbol numbers based upon said first minimum distance between adjacent symbols in the data constellation;
• calculating a second minimum distance between adjacent symbols in the data constellation based upon said first ratio of data constellation symbol numbers;
• and
• calculating additional minimum distances between adjacent symbols in the data constellation and ratios of data constellation symbol numbers until a final minimum distance between adjacent symbols in the data constellation is determined, satisfying system requirements.

A client modem comprising:

• a telephone interface to couple the client modem to a communication channel;
• a symbol table to store a constellation of signals for the communication channel;
• and
• a logic circuit to select constellations and to perform calculations;
• wherein the client modem is to generate data constellations from non-uniform spaced super constellations for exchange of symbols between the client modem and a server modem based upon signals having a bit rate and received from the server modem at the client modem, generating constellations comprising:
• approximating symbol error probability function of a data constellation for an observed noise variance by a function of the ratio between the minimum distance between adjacent symbols in the data constellation and the observed noise variance, multiplied by a density ratio of the data constellation,
• estimating a first minimum distance between adjacent symbols in the data constellation based upon expected symbol error probability selected according to the retransmission overhead of different operation modes;
• calculating a first density ratio of data constellation based upon the first minimum distance;
• and
• directing iterative recalculations of additional density ratios of data constellation and minimum distances between adjacent symbols in the data constellation until a final minimum distance is found that satisfies predetermined system requirements.