4 16 8 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 4 2 6 1 5 3 7 4 0 6 2 5 1 7 3 2 6 0 4 3 7 1 5 6 2 4 0 7 3 5 1 4 0 6 2 5 1 7 3 0 4 2 6 1 5 3 7 6 2 4 0 7 3 5 1 2 6 0 4 3 7 1 5 This is the rate 2/3 Ungerboeck code with 16 states for 8-PSK (natural mapping). The states are defined in Ungerboeck's way. d_free^2 = 2.274^2 Es --> 7.13 dB (so gain of 4.13 dB over uncoded QPSK) Parity check matrix in octal: [16 04 23] Generator Matrix: [ D 1+D+D^2 0 1+D^2 D^2 D]