Information equivalent of relativity

When an observer traveling at near light speeds relative to an observed, then the observed appears to have slow clocks.  Observed events appear more separated in time than one expects. There should be an information theory equivalent to relativity.

 Let's use start with the constant information assumption, the amount of information needed to identify an event is constant.  So, when an observer travels fast relative to the observed, the information describing an event is the same, but the bandwidth of the channel must have increased between observer and observed.  In Shannon theory, the observers, at relative speeds, can see each other with great signal to noise than they can see their own surroundings.  So, even though our channel bandwidth has opened between us, I cannot generate information fast enough to use it efficiently.  Relativity appears as an underencoded channel.