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This paper investigates the quantizer-coder design problem for networked control systems (NCSs) with finite communication bandwidth constraints, where sensors and controllers are connected via digital channels carrying a finite number of bits per unit time. The main purpose is to specify upper and lower bounds of data rates of communication channels, above which there exists a coding and control law for stabilization of linear time-invariant systems. A new quantization and coding scheme to stabilize an unstable plant is proposed. An illustrative example is given to demonstrate the effectiveness of the proposed scheme.