The administrative choice was make that unlike for AMANDA, for IceCube, two Digital Optical Modules should be operated on each  twisted pair of the deployment cable. (A twisted pair is in fact one pair of a twisted quad cable)  There are many reasons for the choice.  The cables themselves don't have to be procured (cost savings of several dollars per foot of cable), the number of hardware channels to be installed in the counting house is reduced by a factor of two, deployment is simplified,  fewer cables need to be modified by the contractor, Seacon Brantner, and a considerable number of flights deploying supplies (tons of cargo) to the south pole are saved by this doubling-up.  The negative consequence is that the electronics complexity increases, the risk of one failure in one module making the data in the other module unavailable exists as a possibility, more complicated wiring harnesses must be developed, the demand on cable bandwidth doubles, and the firmware and software becomes more complicated.  These limitations were deemed not to be show stoppers.

Each cable pairs (transmission line)  exhibits a characteristic impedance, which is constant, and the same for all DOM pairs between the counting house and the place where the pair splits to serve the two digital optical modules.  That splitting imposes a problem.  The obvious (naive) solution of connecting all pairs in parallel at the point they come together is attractive in its simplicity, but has pitfalls.  An argument can be made that the short lengths of the stubs (lines from the split to their respective DOMs) will not introduce electrical problems.   Connecting cables in this way, however,  produces a transmission line mismatch which produces 'impedance bumps' and signal reflections distort the signal.  One can further argue that the mismatch is small, therefore one can ignore errors in the calibration of the electrical length of the cable from surface to DOM caused by this configuration.  These assertions are hard to verify without considerable expenditure of effort and the assembly of a test stand exactly replicating the installed configuration.   The passive, resistive 'splitter', and alternate solution,  wastes DC power, and attenuates the communications signals.  The attenuation of the communications signals reduces the noise margin thereby increasing the bit error rate of the system.

A power splitters/combiners based splitter circuit results in a impedances matching at all three ports, and also features DC power splitting without the IR losses being incurred in a resistive splitter.  The power splitter/combiner solution also affords suppression of the signaling sent from each DOM to the other, while maximizing the coupling to the counting house.  The signal attenuation is also half that of the passive resistor splitter.

The figures below are screen captures from an oscilloscope attached to all three ports of the splitter network under various test conditions.
The objective is to demonstrate that signal output from the ports faithfully reflects the input signal, and the anticipated isolation can be observed.
Furthermore, since the splatters are built around a rather specialized configuration of inductors, the DC current flow must not account for significant signal degradation.

Study of a set of pictures for a pair of 75 ohm power splitters with 0.25 to 300 MHz frequency range.

Study of a set of pictures for a pair of 50 ohm power splitters with 0.004 to 60 MHz frequency range

Comparing the sets of results leads to the conclusion that the 50 ohm splitters will satisfy the electronics requirements for IceCube.

In IceCube the splitter components reside in the 'Octopus' wiring harness which exists between the quad cable break-out at the main cable, and the DOMs.  The Octopus cable harness has connectors for four DOMs, including within it the neighbor coincidence signaling cables for the four DOMs and connectors on the ends to connect to the next neighbor wiring harness to provide
neighbor cable continuity from subgroup to subgroup.

The Octopus wiring harnesses have rubber molded over the places where wires are connected to each other, and to the impedance matching networks.  That means the components either have to be sealed against pressure or have to withstand the pressure at depth.