Combinatorial method of performance calculation in Gilbert-Elliott channels

The Gilbert-Elliott (GE) channel is widely used for modelling the performance of coding and transmission schemes in the context of burst erasure channel conditions. In 1963, Elliott described a mathematical method for calculating the error margins of a GE channel. Though Elliott´s method is used in numerous publications, it has some limitations. One is that it is only suitable for calculating the error rates of single data blocks which makes it not applicable for calculation of error rates of multiple and hierarchical data blocks as applicable for today´s video codecs. Furthermore, this method is based on a recursion formula, which becomes computationally intensive when evaluating large data sets. In this paper, we prove an explicit formula as basis for calculation of error rates in a GE channel which allows calculation of the error rates of multiple and dependent data blocks. The advantages of the proposed method are shown in terms of accuracy for single and multiple data blocks compared to empirical results and in terms of complexity compared to Elliott´s method.