Algorithms for the Communication of Samples

We consider the problem of reverse channel coding, that is, how to simulate a noisy channel over a digital channel efficiently. We propose two new coding schemes with practical advantages over previous approaches. First, we introduce ordered random coding (ORC) which uses a simple trick to reduce the coding cost of previous approaches based on importance sampling. Our derivation also illuminates a connection between these schemes and the so-called Poisson functional representation. Second, we describe a hybrid coding scheme which uses dithered quantization to efficiently communicate samples from distributions with bounded support.