Revision with unchanged content. Digital communications is an important part of modern communications. A digital communication system usually converts analog signals such as voice and video into discrete symbols which can be represented as bits (quantization) and transmits them in a form that can be received reliably. A conventional digital communication system usually transmits all the bits obtained from the quantizer with the same power. In this book, we consider a joint souce-channel coding problem and minimize the end-to-end mean square error distortion (MSE) of a communication system through power allocation to the transmitted bits. This communication system consists of a quantizer with natural binary mapping and Binary Phase Shift Keying (BPSK) modulator at the transmitter and we consider the cases with and without coding. We show that there is an optimal transmit power allocation to the transmitted bits of the quantized word that minimizes MSE.