Union bounds on Viterbi algorithm performance

In the present paper, transform methods (characteristic function techniques) and contour integrals are used to derive a closed-form expression for the performance union bound of a general discrete-time system. It is shown that previously published results may be derived as particular cases of the general formulation developed in this paper. It is well known that the maximum-likelihood Viterbi (1971) algorithm may be employed not only for decoding of convolutional codes but also for optimal detection in other situations. Examples include bandwidth-efficient demodulation, optimal accommodation for inter-symbol interference and cross-channel coupling, test recognition, simultaneous carrier phase recovery and data demodulation, digital magnetic recording, nonlinear estimation, and smoothing. The union bound is a useful measure of the performance of the Viterbi algorithm. Past closed-form expressions for the union bound have usually involved considerable approximation.