Upper Bounds on the Minimum Distance of Trellis Codes

In this paper we are concerned with transmission of digital data using trellis codes to gain some noise immunity over standard uncoded methods. We assume pulse amplitude modulation whereby the values of the transmitted data are estimated from a sequence of samples r 7 generated by a receiver. These output samples are often modeled as rj = xj + nj, (1) where x j is a real number sequence determined by the source sequence of binary data and n j is an independent zero-mean white Gaussian * Bell Laboratories.+ Swarthmore College, Swarthmore, Pennsylvania. ®Copyright 1983, American Telephone & Telegraph Company. Photo reproduction for noncommercial use is permitted without payment of royalty provided that each reproduction is done without alteration and that the Journal reference and copyright notice are included on the first page. The title and abstract, but no other portions, of this paper may be copied or distributed royalty free by computer-based and other information-service systems without further permission. Permission to reproduce or republish any other portion of this paper must be obtained from the Editor. 2617