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

• Published in: IEEE transactions on information theory Vol. 34; no. 3; pp. 435 - 447
• Main Authors: Pottie, G.J., Taylor, D.P.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-05-1988; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; AWGN; Coding, codes; Continuous phase modulation; Convolutional codes; Error correction codes; Exact sciences and technology; Hypercubes; Information, signal and communications theory; Multidimensional systems; Phase shift keying; Quadrature amplitude modulation; Signal and communications theory; Telecommunications and information theory; Upper bound; Phase shift keying; Upper bound; Phase modulation; Convolutional code; Minimal distance; Quadrature modulation; Code
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/18.6024

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.< >