Electronic – mecca ground

For RF signals, the shield carries the signal just as much as the center conductor, and if it is broken anywhere, the cable performance will seriously degrade.

The shield does limit noise, by containing the desired "signal" EM field between the center conductor and the inside of the shield, acting essentially as a Faraday cage, keeping your signal inside, and other signals (noise) outside. The shield is able to completely (ideally) contain the EM field carrying the signal precisely because it carries equal and opposite currents to those in the center conductor at every point along the cable. Were this not the case, there would have to be an external field. Thus, the shield is also the return current path.

The geometry of the shield relative to the center conductor also defines the characteristic impedance of the cable. If there are any discontinuities in the shield, the signal will be distorted by reflections. In the case of the shield being entirely disconnected at one end, the distortions are likely quite horrible, and the power transfer from line driver to receiver will likely be quite poor, as most of the power will be reflected back at the line driver.

M is the number of distinguishable signaling states that the channel can pass, usually modeled as voltage levels.

For example, if you can transmit one of four different voltage levels over a pair of wires, you can send two bits at a time. Eight levels gives your 3 bits, and so on. This is why there's a log₂ relationship between levels and bits.

Distingiushable means that the receiver can reliably determine which of the levels the transmitter is sending. This means that the voltage offsets introduced by noise, intersymbol interference, etc. are less than the actual separation between the signaling levels at the receiver. As the noise level goes up, either you need to increase the overall signal level a corresponding amount, or you need to reduce the number of signaling levels you're using — either way, you increase the separation between the signaling levels.