Improved union bound for Viterbi decoder of convolutional codes

Transmission of binary information sequences over the BSC with crossover probability 0<p 1/2 is considered. It is assumed that a noncatastrophic time-invariant convolutional encoder and Viterbi decoder are used. There are two types of performance characteristics that are usually used to describe the probabilistic behavior of such communication systems. The first type describes the stationary behavior of the system (e.g. bit-error probability, averaged decoding delay, etc.). Usually they are of the main interest. The second type describes the behavior of the system at initial moment (e.g. first-error event probability). The most commonly used “union bounds” to upper bound any of the mentioned characteristics do not take into account some essential difference between these two types of characteristics. We show that standard “union bounds” for stationary characteristics can be considerably improved preserving the same form and terms