Efficient simulation of multidimensional communication systems by sample rejection

Sample rejection has been proposed as an easy-to-implement efficient simulation technique for estimating the probability of decoded bit-error of a communication system. Previous work, however, seems to indicate that sample rejection may be effective only for simulations having small dimensionality, less than 10. While past work has considered a hypersphere rejection region, in this paper, we investigate hypercube and hyperquadrant rejection regions. We assume binary signaling and maximum-likelihood sequence decoding. The results indicate that the knowledge of the minimum Hamming distance of the code and conditioning on the transmitted sequence can be used to improve the gains achievable using sample rejection. The analysis shows that sample rejection can be effective for systems with dimensionality of the order of hundreds with soft-decisions and more than a thousand with hard-decision decoding if the rejection regions are properly chosen.