Item – Theses Canada

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OCLC number
28496066
Author
Kschischang, Frank Robert,1962-
Title
Shaping and coding gain criteria in signal constellation design.
Degree
Ph. D. -- University of Toronto, 1991
Publisher
Ottawa : National Library of Canada = Bibliothèque nationale du Canada, 1992.
Description
3 microfiches.
Notes
University Microfilms order no. UMI00308752.
Includes bibliographical references.
Abstract
This work is concerned with the design and efficient use of multidimensional signal constellations for digital transmission. Multidimensional constellations can be viewed as coded modulation schemes that can increase signal-to-noise ratio (SNR) efficiency relative to their two-dimensional (2D) counterparts. The SNR efficiency of multidimensional constellations designed by taking the intersection of a finite region $\IR$ in N-space with the sphere centers in a dense packing of spheres is governed both by the choice of the region $\IR$ (which can give a shaping gain) and by the choice of the sphere packing (which can give a coding gain). Shaping gain results from energy savings obtained by selecting constellation points with low energy more often than points with high energy. In this work, a family of distributions that achieve the best possible tradeoff between bit rate and average transmitted energy is derived. An asymptotically accurate "continuous approximation" furnishes a quantitative analysis and insight into the tradeoffs involved with nonuniform signalling. Methods of achieving practical nonuniform schemes by mapping variable-length prefix condition codes onto signal constellations are studied and several examples of combining nonuniform signalling with trellis coding are given. Under uniform signalling, maximum possible shaping gain is obtained by choosing a spherical region $\IR$, but at the expense of large 2D constellation expansion ratio (CER) and large 2D peak-to-average energy ratio (PAR). In this work, the shaping gain of a family of regions called truncated polydiscs is derived, and it is shown that these regions achieve maximum shaping gain for a given PAR or CER. An efficient algorithm for mapping datawords to constellation points is described. To achieve coding gain, dense sphere packings are constructed from ternary and quaternary codes. Results include: (a) tables of the best ternary and quaternary constacyclic codes up to block length 50, (b) the $(u + v + w \vert 2u + v\vert u)$ construction, a ternary code construction technique, and (c) tables of linear ternary and quaternary codes obtained by modifying and combining various codes discovered here and in the literature. Using these codes, sphere packings are generated in even dimensions up to 100. In dimensions 36 and 60, new record densities appear to have been achieved.
ISBN
0315692375
9780315692374