Sphere-packing upper bounds on the free distance of trellis codes

Author

Pottie, Gregory J. ; Taylor, Desmond P.

Author_Institution

Dept. of Electr. & Comput. Eng., McMaster Univ., Hamilton, Ont., Canada

Volume

34

Issue

3

fYear

1988

fDate

5/1/1988 12:00:00 AM

Firstpage

435

Lastpage

447

Abstract

Sphere-packing arguments are used to develop upper bounds on the free distance of trellis codes. A general bounding procedure is presented. Sphere packing bounds, including bounds on the density of infinite regions, packings for hypercubes, and packings on the surface of a unit sphere, are then used to produce bounds for a wide variety of trellis codes. Among the applications are convolutional codes, Ungerboeck codes for phase-shift keying and quadrature amplitude modulation, coset codes, and continuous phase modulation codes. The new bounds are significantly tighter than existing bounds in many cases of practical interest

Keywords

encoding; error correction codes; Ungerboeck codes; continuous phase modulation codes; convolutional codes; coset codes; free distance; phase-shift keying; quadrature amplitude modulation; sphere packing bounds; trellis codes; upper bounds; AWGN; Continuous phase modulation; Convolutional codes; Error correction codes; Helium; Hypercubes; Multidimensional systems; Phase shift keying; Quadrature amplitude modulation; Upper bound;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.6024

Filename

6024