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This book describes mathematical methods for analyzing digital transmission system performance. In contrast with publications that use an idealistic model of channels with independent errors, this book shows how to evaluate performance characteristics of information transmission systems in real communication channels with bursts of noise. The book shows how to apply hidden Markov Models (HMMs) to model and analyze performance of communications systems (including error correction codes and communication protocols) in channels with memory. This edition includes a new chapter describing the theory and applications of continuous state HMMs. Methods developed in the book have broad applications in queuing theory, speech and image recognition, signature verification, control theory, artificial intelligence, biology, fraud detection, and finance. The attached CD-ROM contains numerous MATLAB programs implementing the theory described in the book. With a rich assortment of chapter-ending problems and illustrations, the book and CD-ROM are perfect tools for the study of HMM methods or for use as a classroom text.