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The Universal Mobile Telecommunication System (UMTS) adopts WCDMA as the air interface that provides variable transmission rate services. Four traffic classes are identified in UMTS, given as controversial, streaming, interactive, and background classes. To efficiently utilize the radio bandwidth, the shared channel technology is proposed to deliver interactive and background traffics. This paper proposes a "shared-channel assignment and scheduling" (SCAS) algorithm to allocate shared channels to interactive and background connections. We formally prove that the SCAS algorithm can satisfy the transmission rate requirement of each interactive connection and can efficiently utilize the radio bandwidth.