Communications

Light speed round trip between Earth and Mars is between 3 and 22 minutes each way

Currently all communications to Mars from Earth are via NASA's Deep Space Network and also uses the Satellites currently in orbit around Mars to greatly enhance data rates, consern over the 13 year old 'Mars Odyssey orbiter' would just leave MAVEN satellite as an emergency backup due to its highly elliptical orbit .

NASA "The data rate direct-to-Earth varies from about 500 bits per second to 32,000 bits per second (roughly half as fast as a standard home modem). The data rate to the Mars Reconnaissance Orbiter is selected automatically and continuously during communications and can be as high as 2 million bits per second. The data rate to the Odyssey orbiter is a selectable 128,000 or 256,000 bits per second (4-8 times faster than a home modem)."

 Odyssey

ESA have a limited DSN that works well to Earths moon, below is a very good introduction to how Deep Space Network's function 

Earth Mars conjunction 

Once every 26 months, the Sun is exactly in between Mars and the Earth( conjunction) . This occultation lasts about six weeks that arises also to the maximum signal delay of 22 minutes. 

Proposals

To use two communications satellite in polar orbit around the Sun to relay signals during this period.

NASA lasers Communications

For Artims 2 test mission to the orbit the Moon it plans to use a Lasers downlink

XCOM

NASA is working on using X-rays to communicate in space X-ray communications in space is called XCOM.

X-rays have much shorter wavelengths than both infrared and radio. This means that, in principle, XCOM can send more data for the same amount of transmission power. The X-rays can broadcast in tighter beams, thus using less energy when communicating over vast distances. Gigabytes-per-second data transmission throughout the solar system. the narrow beams could mean that many of them can be used in parallel.

One big advantage that XCOM has over other forms of communications is the ability to transcend obstacles that usually hinder radio communication. Whenever a spacecraft is entering the atmosphere at hypersonic speeds, it generates an intensely hot plasma cover that blocks radio waves that  acts as a shield, cutting off radio frequency communications with anything outside the vehicle for several seconds 'radio blackout' during re-entry. as far as human spaceflight is concerned, X-rays can pierce the hot plasma sheath that builds up as spacecraft hurdle through Earth’s atmosphere at these hypersonic speeds.

NASA recently launched an XCOM test system to the ISS on the SpaceX CRS-17 (Commercial Resupply Service-17) Dragon resupply on 4th of May 2019.  This NASA XCOM test uses a Modulated X-ray Source(MXS) that most importantly is low-cost, in the form of a miniature x-ray source has been developed that can be modulated in intensity from completely off to full intensity on nanosecond timescales. The two days of testing on the ISS were successful.

Gamma ray communication

In the more distant future gamma rays could be used.

A two-millisecond gamma ray burst could carry 1,000,000,000,000,000,000 (1x10 to the power of 18) bits of information, that is equivalent to a data rate 500 Million Terabytes per second if it could be sustained.

 “So far as we know, gamma rays offer the widest practical communications bandwidth in the electro-magnetic spectrum and the only feasible way to send large quantities of information over intergalactic distances.” Dr John A. Ball (MIT)