It is a great pleasure to be asked to write the Preface for this book on trellis decoding of error correcting block codes. The subject is extremely significant both theoretically and practically, and is very timely because of recent devel- opments in the microelectronic implementation and range of application of error-control coding systems based on block codes. The authors have been notably active in signal processing and coding research and development for several years, and therefore very well placed to contribute to the state of the art on the subject of trellis decoding. In particular, the book represents a unique approach to many practical aspects of the topic. As the authors point out, there are two main classes of error control codes: block codes and convolutinal codes. Block codes came first historically and have a well-developed mathematical structure. Convolutional codes come later, and have developed heuristically, though a more formal treatment has emerged via recent developments in the theory of symbolic dynamics. Max- imum likelihood (ML) decoding of powerful codes in both these classes is computationally complex in the general case; that is, ML decoding fails into the class of NP-hard computational problems. This arieses because the de- coding complexity is an exponential function of key parameters of the code.
To Christians, Jesus of Nazareth is the pivotal figure in human history. The entire Bible is about Him. Passages in the Old Testament forecast His life. In some Scriptures, references to Jesus are clear. In others, biblical writers relied on symbolism to foretell Jesus's time on earth.
In his book Decoding Bible Messages, author John A. Mapp Jr. shines a laser on the Old Testament. Mapp provides numerous examples to bring Jesus out of the symbolism used by Old Testament writers. Passages that, at first look, seemed to have nothing to do with Jesus take on new meaning. For example, Mapp explains how the manner in which the Passover lamb was slaughtered is a symbolic portrayal of Jesus's crucifixion. Through Mapp's research, you'll discover the Old Testament is truly a hologram of Jesus Christ.
Decoding Bible Messages provides a new perspective on the Old Testament. Learn to see Jesus on every page, and in the process, gain a new appreciation of the inspired nature of the whole Bible, plus a deeper revelation of the sovereign hand of God.
Coding with Modifiers uses real-life modifier scenarios and medical records to guide correct CPTr and HCPCS modifier usage. Readers can also learn how and when to use modifiers to avoid expensive delays and denials. How and When to Use Modifiers Coding with Modifiers is required reading for anyone that uses claim modifiers on a regular basis. This fifth edition uses the revised modifier guidelines to instruct the reader how and when to use modifiers. Real-life modifier scenarios aid the implementation of modifier guidelines.
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