Information infrastructure includes communications for Mars and communications with Earth. Facilities for information infrastructure would include communication antennas and server farms. These are linked by communication systems that may be physical or wireless.
For an objective of continuous communications with Earth a typical architecture might require a Mars ground base station, a Mars geostationary transmitter/receiver, a repeater on a Mars co-orbit to act as a relay station while Mars is behind the Sun. An Earth geostationary transmitter/receiver and an Earth ground station. Additional infrastructure might be required to communicate with vehicles in transit between the two planets.
Server farms with extensive data storage would be required on Mars due to the problem of Latency between Earth and Mars. Terabytes of storage would be required for video feeds, entertainment storage, technical data and communications. Multiple Terabyte drives massing less than a kilogram each are available off the shelf. A single terrabyte represents about 250 x 2 hours movies, or about 20 high definition movies. Petabyte storage elements (1000 terabytes) are also available, and a container's worth of drives, holding 100 petabytes or more, is available from Amazon. The heat from the Amazon system requires 350 kW of cooling. One single of these might be enough for the initial settlement development for a fairly important population.
Interplanetary Internet can be used as a platform for communications with Earth.