Sample rejection for efficient simulation of binary coding schemes over quantized additive white Gaussian noise channels

We re-examine sample rejection (SR), introduced previously as an easy-to-implement efficient simulation technique. Since the decoding operation often represents a major part of the required simulation time, SR can be used to avoid decoding of the received sequences that are known beforehand to be decoded error-free. Previous work seems to indicate that SR may be effective only for simulations having small dimensionality, less than 10. We assume estimation of decoded bit-error probabilities for a general coding scheme of finite block length transmitted over an additive white Gaussian noise channel with quantized output using binary antipodal signaling and maximum-likelihood sequence decoding. We show that knowledge of the minimum Hamming distance of the code and conditioning on the transmitted sequence can be exploited to form the rejection regions. In particular, we investigate hypersphere, hypercube, and hyperquadrant rejection regions. Our analysis shows that SR can be effective for some systems with dimensionality on the order of hundreds with soft-decision decoding, and some systems with dimensionality more than a thousand with hard-decision decoding if the rejection regions are properly chosen.