Some distance properties of convolutional codes.

Abstract

Various representations of convolutional codes useful in analyzing distance properties are presented. Row distance, column distance, minimum distance, and free distance are defined. Known bounds on these distances are summarized, and where instructive, the methods of proof are indicated. A novel approach to the distance structure of a code is given in the form of a plot of row distance and column distance against depth into the code trellis. Bounds on minimum distance are applied to determine behavior of row and column distance. Finally, the problem of determining the length of sequence necessary to produce the minimum weight codeword is considered. A bound for systematic codes is presented. This bound appears to be the tightest bound on this length presently known.