  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.
