A practical approach for determining burst error distributions for convolutional codes

In evaluating the performance of concatenated error-correction codes, it is useful to know the error statistics at the inner code output. A common inner code is a convolutional code. Methods for characterizing the output error statistics for convolutional codes do exist, but the computational effort required grows exponentially with the constraint length. This paper presents a computationally feasible method for characterizing error statistics output from any convolutional code. Specifically, a technique for determining the error statistics for a k=3, rate ¹/₃ and a k=7, rate ½ convolutional encoder is discussed. An error state diagram is utilized to derive discrete state equations necessary to solve for the transfer function in terms of trellis transition probabilities. Work presented by Best can be manipulated to yield theoretical transition probabilities, but doing so is not computationally practical. Results presented in this paper are based on using empirical trellis transition probabilities in the transfer function