Abstract
A fundamental problem in digital communications is the corruption of the transmitted signal by noise. The minimum-distance philosophy for receiver design is reasonably robust in the presence of noise, but two questions arise: when is it optimal? And what should be done when it is not? In this chapter we start with the statistics of the noise and develop a theory of optimal detection for both discrete-time and continuous-time channels. With this theory, we identify the circumstances under which the minimum-distance receiver is optimal. Moreover, we take a systematic approach to receiver design based on a probabilistic characterization of the noise that is applicable to a wide range of applications beyond the classical model of additive white Gaussian noise, including those for which minimizing distance is not optimal. The probabilistic tools developed in this chapter play an important role in iterative decoding of error-control codes (Chapter 12)
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© 2004 Springer Science+Business Media New York
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Barry, J.R., Lee, E.A., Messerschmitt, D.G. (2004). Probabilistic Detection. In: Digital Communication. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0227-2_7
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DOI: https://doi.org/10.1007/978-1-4615-0227-2_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-4975-4
Online ISBN: 978-1-4615-0227-2
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