l theorems due to Claude transfer the data generated by an information source Shannon: the noiseless coding theorem [45], the efficiently and reliably over a noisy channel. The basic source coding theorem [46], the channel coding theorem components of a digital communication system are [45], and the source-channel coding theorem [46]. Our shown in Figure 3.4-1: a source encoder, channel en- exposition mainly follows that of McEliece [17], where coder, modulator, demodulator, channel decoder, and proofs of the theorems can be found. For simplicity, we source decoder. focus on discrete memoryless sources and channels. The source encoder removes the redundancy in the References are provided for extensions and generaliza- digital data produced by the information source and out- tions. Shannon's coding theorems give an insight on puts an information sequence. If the information source is what can be achieved by a communication system. analog, its output must be digitized before it is processed Unfortunately, the theorems are not constructive. Opti- by the source encoder. The channel encoder adds re- mal codes were shown to exist, but it was not explained dundancy to the information sequence SO that channel how to construct them. The remainder of the chapter is errors can be detected or corrected. The output of the dedicated to practical system design. Section 3.4.3 con- channel encoder is a finite sequence of symbols called tains an overview of the most important channel codes. a channel codeword. The set of possible channel code- Section 3.4.4 reviews state-of-the-art modulation words is called a channel code. The modulator maps the techniques, focusing on a promising method called channel codeword to a signal that is suitable for trans- hierarchical modulation. Section 3.4.5 considers com- mission over a physical channel. The demodulator con- munication systems where feedback information can be verts the received signal into a discrete sequence of real sent from the receiver to the transmitter. In this situation, nu