Information is passed through optical fibers in a way that isn't vastly different than AM radio. A carrier frequency is chosen (corresponding to a free-space wavelength of light of around 1.55 microns, in the near-infrared) that just so happens to correspond to the frequency where the optical absorption of ultrapure SiO2 glass is minimized. Light at that frequency is generated by a diode laser, and the intensity of that light is modulated at high speed (say 10 GHz or 40 GHz), to encode the 1s and 0s of digital information. If you look at the power vs. frequency for the modulated signal, you get something like what is shown in the figure - the central carrier frequency, with sidebands offset by the modulation frequency. The faster the modulation, the farther apart the sidebands. In current practice, a number of carrier frequencies (colors) are used, all close to the minimum in the fiber absorption, and the carriers are offset enough that the sidebands from modulation don't run into each other. Since the glass is very nearly a linear medium, we can generally use superposition nicely and have those different colors all in there without them affecting each other (much).
So, if you want to improve data carrying capacity (including signal-to-noise), what can you do? You could imagine packing in as many channels as possible, modulated as fast as possible to avoid cross-channel interference, and cranking up the laser power so that the signal size is big. One problem, though, is that while the ultrapure silica glass is really good stuff, it's not perfectly linear, and it has dispersion: The propagation speed of different colors is slightly different, and it's affected by the intensity of the different colors. This tends to limit the total amount of power you can put in without the signals degrading each other (that is, channel A effectively acts like a phase and amplitude noise source for channel B). What the UCSD researchers have apparently figured out is, if you start with the different channels coherently synced, then the way the channels couple to each other is mathematically nicely determined, and can be de-convolved later on, essentially cutting down on the effective interference. This could boost total information carrying capacity by quite a bit - very neat.