This book provides an accessible introduction to the theoretical foundations of modern coding theory, with many applications to wireless transmission systems. State-of-the-art coding theory is explained based on soft (maximum-likelihood) decoding rather than on algebraic decoding. Convolutional codes, trellis-coded modulation, turbo codes, and low-density parity-check (LDPC) codes are covered, with specific reference to the graphical structures through which they can be described and decoded (trellises and factor graphs). A special section addresses multiple-antenna systems and space-time codes.