Abstract: A 14.4 kilobit/second modem uses an encoding scheme in which groups of five bits are encoded as one of thirty-two (2.sup.5) possible code groups. This is done by using quadrature amplitude modulation and a 6 by 6 space-state constellation which allows a maximum of thirty-six different points to be encoded. Since only thirty-two points are needed the four outer corner points of the constellation are not used. In order to achieve the desired 14.4 KBPS data rate the baud clock must run at 2880 Hz. However, this bandwidth is very close to the maximum bandwidth available on voice-grade telephone lines. Accordingly, data encoding and data recovery techniques must be used which maximize the probabilities of correctly receiving the encoded data signals.