Table 1: Comparison of complexity of message representations, where 𝑅 is the number samples taken from each distribution and 𝑀 is the number of distributions or messages.

Operation Complexity Value of 𝑅

Discretized Filtering 𝒪 ( 𝑅 2 ) Large
Discretized Multiplication 𝒪 ( 𝑅 𝑀 ) Large
Sample-based Filtering 𝒪 ( 𝑅 ) Small
Sample-based Multiplication 𝒪 ( 𝑅 2 𝑀 ) Small
Parametric Filtering 𝒪 ( 𝑅 ) Small
Parametric Multiplication 𝒪 ( 𝑅 𝑀 ) Small