We consider a variant of the channel simulation problem with a single input and multiple outputs . We show that the growth rate of theexpected codeword length is sub-linear in $n$ when a power law bound is satisfied . An application of multiple-outputs channel simulation is thecompression of probability distributions . This can also be regarded as a lossy compression setting for probability distributions, such as adistribution over positive integers and continuous distribution over $[0,\infty)$ with a non-increasing pdf . This paper describes encoding schemes for three cases of $P$: $P is adistributed over positive integer numbers,$P \$ is a continuous distribution

Author(s) : Chak Fung Choi, Cheuk Ting Li