In the current paradigm, TV white space databases communicate the available channels over a reliable Internet connection to the secondary devices. For places where an Internet connection is not available, such as in developing countries, a broadcast based geolocation database can be considered. This geolocation database will broadcast the TV white space (or the primary services protection regions) on rate-constrained digital channel. In this work, the quantization or digital representation of protection regions is considered for rate-constrained broadcast geolocation database. Protection regions should not be declared as white space regions due to the quantization error. In this work, circular and basis based approximations are presented for quantizing the protection regions. In circular approximation, quantization design algorithms are presented to protect the primary from quantization error while minimizing the white space area declared as protected region. An efficient quantizer design algorithm is presented in this case. For basis based approximations, an efficient method to represent the protection regions by an `envelope' is developed. By design this envelope is a sparse approximation, i.e., it has lesser number of non-zero coefficients in the basis when compared to the original protection region. The approximation methods presented in this work are tested using three experimental data-sets.