“…D IGITAL communications systems are currently being developed for high-bit rate transmission over bandlimited channels. These applications include asymmetric digital subscriber loop [8], [22] (ADSL), high-speed digital subscriber loop (HDSL) [20], [26], [45], very high-speed digital subscriber loop (VHDSL) [7], [17], ATM-LAN [18] and interactive multimedia television (IMTV) [19], high-density magnetic recording [9], wireless systems [1], and digital highdefinition TV (HDTV) transmission [29], [30]. In each of these applications, the bandlimited nature of the channel and the required performance levels necessitate the use of highly complex digital communications algorithms.…”