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6 - Infinite constellation for modulation

Published online by Cambridge University Press:  05 August 2014

Ram Zamir
With contributions by
Bobak Nazer  and
Yuval Kochman
Illustrated by
Ilai Bistritz
Ram Zamir
Affiliation:
Tel-Aviv University
Bobak Nazer
Affiliation:
Boston University
Yuval Kochman
Affiliation:
Hebrew University of Jerusalem
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Summary

Digital communication is the process of encoding an information source and sending it digitally over a noisy channel. Chapter 5 dealt with the source coding part: digitization of an analog signal using a lattice quantizer. In this chapter we shall consider the channel coding part: translation of digital information into an analog signal via lattice modulation, and detection of the information from a noisy version of the signal with a small probability of error.

In lattice modulation, the lattice points form the signal constellation, or codebook, where each lattice point carries a different message (Sections 1.1 and 3.3). Popular examples are pulse-amplitude modulation (PAM) and quadrature-amplitude modulation (QAM), which correspond to one-dimensional and two-dimensional lattice-like constellations. A general approach to constructing multi-dimensional lattice constellations is by shaping, i.e., by cutting a finite section from a lattice. The most popular shapes are a cube (uncoded constellation), a ball (spherical shaping) or the Voronoi cell of some coarse lattice (Voronoi shaping), as we shall see in Chapter 9.

In this chapter we want to keep the lattice unbounded – just as for the dithered lattice quantizer of Chapter 5. Thus we are faced with a problem: how do we define the transmission power and the coding rate of an infinite constellation?

Type
Chapter
Information
Lattice Coding for Signals and Networks
A Structured Coding Approach to Quantization, Modulation and Multiuser Information Theory
 , pp. 110 - 133
Publisher: Cambridge University Press
Print publication year: 2014

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