2 each pam symbol respectively contains 4 3 2 and 1 bit of information each symbol of the corresponding four dimensional s4d p m i symbol sets contains 16 12 8 and 4 bits of information it is noted that for each decrease in k by 1 an amplitude difference between symbols in a symbol set s4d p m i is doubled making it is easier to differentiate between symbols transmitted between transceiver 21 and 31 and improving the signal to mean squared error mse ratio of slicers in the transceivers used in determining which symbols is received by the transceivers signal to mse ratio mser is defined by an expression mser 10 log 10 d 2 2 e e 2 where d is a minimal distance between slicer decision levels and e e 2 is a mean of the squared slicer error signal at the decision levels as a result for each decrease in k by 1 d doubles and the mser improves by 6 db assuming additive white gaussian noise awgn in the channel coupling transceivers 21 and 31 for a given level of noise in the channel improvement in mser by 6 db substantially improves a symbol error rate ser in symbols transmitted between the transceivers for example assuming a ser of 10 u2212 5 a 6 db improvement in mse improves the ser to 10 u2212 17 and sers of 10 u2212 7 and 10 u2212 9 are improved to 10 u2212 25 and 10 u2212 32 respectively the inventors have determined that the improvement in ser provided by reducing i by 1 provides about a same improvement in ser for a awgn channel as is provided by encoding data in accordance with a reed solomon rs code having an.