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.
展开▼
