Information-theoretic measure of resilience-to-noise

A bit of information in one place and time is transferred both spatially and temporally, but how far? One important influence is 'noise' or 'randomness' such as temperature in Ising-spin systems, or packet loss in router networks. Using the definitions of information dissipation length (IDL, spatial) and information dissipation time (IDT, temporal) you will define a novel measure of 'resilience-to-noise' from the viewpoint of information processing. The measure should be based on how fast the IDT or IDL diminishes as function of increasing 'noise'.