Two major error control techniques are used for digital information transmission over noisy channels: block codes (linear and cyclic) and convolutional codes. In the 1970s, the idea of trellis decoding of block codes appeared. This technique for error detection and correction has become important for its significant performance improvement in existing communication and information systems, such as mobile and personal radio systems and magnetic and optical storage devices.

The complexity of trellis decoders can be minimized by an appropriate coordinate reordering in the code table, as discussed in chapter 2. Such a reordering can be obtained as a generalized array decomposition, which is equivalent to the coset decomposition of the code. The concept of generalized array codes (GACs) was introduced by the authors. This novel technique allows an array decomposition of block codes and can be used for the design of their trellis decoders. The most widely used binary block codes (such as Hamming, Reed-Muller, BCH, and Golay) have been constructed in the GAC format. In addition, a practical solution that allows the design of run-length limited and balanced codes by a simple modification of the parent block code is introduced.

Chapter 3 presents a novel trellis decoding procedure for both array codes and GACs. The authors prove that the designed trellises are minimal and show a potential performance enhancement. This discussion is supported by three software packages that graphically illustrate both trellis design procedure for different block codes and the application of the Viterbi decoding algorithm for these codes. This software is available only from the authors. A similar procedure is applied to the trellis design of run-length limited and balanced codes. It is emphasized that, since these codes represent a class of nonlinear block codes, no other known technique can be used for such a design.

In chapter 4, a number of adaptive coding schemes in which a single encoder and soft maximum likelihood trellis decoder provide different levels of error performance, adaptiveness, and overall implementation complexity are proposed. A novel technique called nested trellis decoding is introduced.

Chapter 5 considers Reed-Solomon (RS) codes as a particular case of block codes. As with binary block codes, trellis decoders for RS codes can be designed based on syndrome or coset trellises. Because there are some limitations that make the practical implementation of such decoders infeasible, an array decomposition of RS codes is proposed, together with a novel technique called the Shannon product of trellises. This technique allows for the easy design of both syndrome and coset trellises for RS codes and provides a basis for the development of efficient low-complexity trellis decoders. Finally, this chapter contains a near-maximum-likelihood two-stage trellis decoding algorithm for RS codes.

In recent years, one of the major achievements of the theory of error control coding has been the introduction and development of multifunctional coding. This term is applied to a system designed to perform two or more simultaneous functions within the overall architecture of a communication system, such as error control, modulation, synchronization, and channel estimation. In chapter 6, the concept of multifunctional trellis decoding is introduced and formalized. Multifunctional trellis decoding seeks to amalgamate as many of the receiver functions as possible into a single integrated procedure, with the objectives of improved overall system performance and economy of implementation. The authors consider soft maximum likelihood trellis decoding, demodulation, synchronization (at the bit, symbol, and block levels), and real-time channel estimation.

This book is aimed at undergraduate and graduate students, communication engineers, and researchers working in the area of control coding. It is a good book about the basic principles of trellis decoding for block codes, existing open problems, some recent solutions, and different applications of this technique.