Abstract
In this chapter we introduce signal constellations as sets S = {x} of vectors in an n-dimensional space. Codes in signal spaces are defined as constellations whose elements are n-tuples of “elementary signals” chosen in a set X. We evaluate the error probability obtained when a code in a signal space is used for transmission over the additive while Gaussian noise channel. Constellalions are then compared on the basis of their bandwidth and power efficiencies. Capacity theorems yield ultimate bounds on the achievable performance. Next, we examine some symmetry properties of signal sets. A class of codes having a special algebraic structure, viz., linear binary codes, is introduced and described in some depth.
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(2005). Coding in a signal space. In: Coding for Wireless Channels. Information Technology: Transmission, Processing and Storage. Springer, Boston, MA. https://doi.org/10.1007/1-4020-8084-0_3
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DOI: https://doi.org/10.1007/1-4020-8084-0_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4020-8083-8
Online ISBN: 978-1-4020-8084-5
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