We consider a linear quadtric Gaussian (LQG) networked control setting where the sensor and the controller are separated by a fixed-rate noisless channel. For this setting, the minimal rate required to stabilize the system is known. In this talk, we concentrate on minimizing the LQG cost for the scalar case. To that end, we use the Lloyd-Max algorithm and properties of log-concave functions to construct the optimal greedy quantizer at every time instant, which varies according to the previous quantized measurement values. To construct the globally optimal scheme, we extend the algorithm by connecting it to the problem of scalar successive refinement. We conclude by discussing extensions to the vector case.