We develop a joint source-channel coding (JSCC) scheme based on an unequal power allocation strategy, in which different levels of power are allocated according to a priori probability distribution of the information bits. Two protograph low-density parity-check codes are used as the source code and the channel code, respectively, in the proposed JSCC scheme. With fixed row weight and row element alphabet, optimization on the source code is conducted via random search to obtain a best-found base matrix with the lowest decoding threshold among all the searched base matrices. Simulation results show that the new JSCC scheme outperforms the traditional equal power allocation-based JSCC by exploiting the source statistics at the decoder. Moreover, theoretical threshold analysis is in agreement with the practical simulation results.