Distance Properties of Convolutional Codes

This chapter is devoted to a flurry of distances of convolutional codes. Properties of convolutional codes via the active distances are elaborated, and the distances of cascaded concatenated codes are analyzed. Several important distance measures for convolutional codes and encoders are defined, and time-varying convolutional codes are introduced. Upper bounds on the free distance and lower bound on the distance profile are derived. The Viterbi (distance) spectrum for a convolutional encoder is obtained via the path enumerators that are determined from the state-transition diagram for the encoder in controller canonical form. It has been explained that the zero state driving information sequence for a rational generator matrix with a given encoder realized in controller canonical form is the sequence of information tuples that causes the memory elements to be successively filled with zeros.