Error Detecting Codes

Error detecting codes are very popular for error control in practical systems for two reasons. First, such codes can be used to provide any desired reliability of communication over any noisy channel. Second, implementation is usually much simpler than for a system using error correcting codes. To consider a particular code for use in such a system, it is very important to be able to calculate or estimate the probability of undetected error. For the binary symmetric channel, the probability of undetected error can be expressed in terms of the weight distribution of the code. The first part of the book gives a detailed description of all known methods to calculate or estimate the probability of undetected error, for the binary symmetric channel in particular, but a number of other channel models are also considered. The second part of the book describes a number of protocols for feedback communication systems (ARQ systems), with methods for optimal choice of error detecting codes for the protocols.
Results have been collected from many sources and given a unified presentation. The results are presented in a form which make them accessible to the telecommunication system designer as well as the coding theory researcher and student. The system designer may find the presentation of CRC codes as well as the system performance analysis techniques particularly useful. The coding theorist will find a detailed account of a part of coding theory which is usually just mentioned in most text books and which contains a number of interesting and useful results as well as many challenging open problems.
Audience: Essential for students, practitioners and researchers working in communications and coding theory. An excellent text for an advanced course on the subject.

PREFACE.- 1 CHANNEL MODELS.- 1.1 Introduction.- 1.2 Channels Without Memory.- 1.3 Channels With Memory.- 1.4 Channel Transforms.- 1.5 Comments and References.- 2 BASICS ON ERROR CONTROL.- 2.1 ABC on Linear Codes.- 2.2 Weight Distributions.- 2.3 Principles of Error Detection.- 2.4 Combined Correction and Detection.- 2.5 Comments and References.- 3 ERROR DETECTING CODES FOR THE BSC.- 3.1 Basic Formulas and Bounds.- 3.2 Finding the Average.- 3.3 The Worst-Case Error Probability.- 3.4 P1e for a Linear Code and its Dual.- 3.5 General Bounds.- 3.6 Optimal Codes.- 3.7 New Codes from Old.- 3.8 Combined Correction and Detection.- 3.9 Complexity of Computing Pue(C, p).- 3.10 Particular Codes.- 3.11 How to Find the Code You Need.- 3.12 Comments and References.- 4 CODES FOR OTHER CHANNELS.- 4.1 The Z-channel.- 4.2 Channels With Memory.- 4.3 Conclusions.- 4.4 Comments and References.- 5 PROTOCOLS.- 5.1 Introduction..- 5.2 The Main Criteria of FS Efficiency.- 5.3 Basic Protocols for Decision Feedback Systems.- 5.4 Protocols With Information Feedback.- 5.5 Conclusions.- 5.6 Appendix: Signal Flow Graphs for Protocol Analysis.- 5.7 Comments and References.- 6 CODE OPTIMIZATION.- 6.1 Basic Criteria for Optimization.- 6.2 Channels Without Memory.- 6.3 Channels With Memory.- 6.4 Iterative and Concatenated Codes.- 6.5 Optimization of Protocols.- 6.6 Comments and References.- 7 CONCLUDING REMARKS.- REFERENCES.