I've heard a lot of people talk about sending a probe to Enceladus (one of Saturn's natural satellites). It would drill (or melt ice) to burrow through the thick layer of ice and get to the water below in an attempt to find life. If the thickness of Enceladus' ice shell could be hundreds of meters thick, how will the probe communicate its findings back to us? Will it be able to effectively communicate through the ice?
I don't know about multiple mission proposals, but I was able to find a fairly well spelled-out plan so I'll answer based on that. The proposal is based on the IceMole melting probe but I don't know if there's a name for the proposal itself.
The best source of data I've found is this PDF from 2014.
It indicates that at least for this proposed mission they wouldn't be building a full-on submarine that would drop into the sub-ice ocean, but instead they'd burrow down to the side of a geyser to sample the water from it:
Analysis of the plume material strongly suggests that it originates from a body of liquid salt-water or even a global ocean below the icy crust. The unique chemistry found in the plumes has fueled speculation that Enceladus may harbor life. A lander mission equipped with a subsurface ice-melting probe may help to resolve this question. Landing on the rough terrain close to the tiger-stripe cracks from which the plumes emanate, however, is considered highly risky (see Fig. 2), so a probe that lands at a safe distance from a crack and melts its way to the inner wall to analyze the plume material in situ would be desirable.
(In-line references removed for quotability, see paper for more details)
That simplifies things in terms of communication: only burrowing a short distance and not leaving the tunnel make a tether entirely reasonable. In this proposal the tether would carry both communications from the probe and power to the probe, which also simplifies the design by only requiring one power source instead of a power source for the base station and a separate power source for the probe.
This may be in reference to the use of the probe in the antarctic, but it indicates that they've made plans for reasonably long distances (though not to the scale required to go completely through 30-40 km of ice shelf over the expected liquid water):
For greater depths of several hundred meters, the cable can be packed into separate containers (each containing several tens of meters of cable) that are added to the IceMole.
Although I and many other authors of the 2007 Enceladus study would love to see such a mission happen, that seems very unlikely in the near future. The first issue is that Enceladus orbits only four Saturn radii out, so is in a very deep gravitational well. Second, assuming the probe orbits with its pariapsis at Enceladus and its apoapsis at Titan, the relative speed when passing by Enceladus would be about 4 km/sec.
The distance to the Saturn system compared to Jupiter's and the deep gravity well means a lot more fuel and gravity assists, which translates into more $$. The distance and number of gravity assists also makes arrival at Saturn something like ten years after launch, which is longer that the nominal life of many of the components. The principle advantage, compared to Europa, is Enceladus squirts samples of its (presumed) ocean out into space. The large relative speed of the orbiter relative to Enceladus' surface limits the mass that can be slowed down enough to survive landing (using an ATK STAR series solid rocket motor).
I was interested to read about the IceMole referenced in 1227joe's answer. However, it seems to me it would be very challenging to include one on an Enceladus mission. The power requirement for the proposed EnEx-IceMole is on the order of 10 KW. Solar flux at Saturn is only 1.1% of that at Earth and RTGs (Radioisotope Thermoelectric Generators), like those used on Cassini and New Horizons, only put out a little over 200 watts each.
The primary ways proposed to search for biomarkers (or life itself) was to sample the effluent from the tiger strips from orbit or buried in the snow just under the surface with a drill on a lander. Since there would be no deep drilling, the only communication would be in data bursts from the lander when the probe passed by that would eventually be relayed to Earth.
Lastly, there was another proposed mission, TANDEM, that, initially, was planned to study both Titan and Enceladus (hence the name). However, it morphed into primarily a Titan mission with maybe some flybys of Enceladus. The coolest thing about the mission was its proposed nuclear powered Montgolfiere that would float over Titan's surface! The proposal was dropped in 2009 when a (much less expensive) Jupiter/Europa mission was chosen as the primary effort.
Link to Enceladus Study Final Report (thanks TildalWave):
ESA/NASA proposed TANDEM mission: