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

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2 Author(s)
Pottie, G.J. ; Dept. of Electr. & Comput. Eng., McMaster Univ., Hamilton, Ont., Canada ; Taylor, D.P.

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

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Information Theory, IEEE Transactions on  (Volume:34 ,  Issue: 3 )