How does widening the frequency band allows us to make faster pulses in a radio link?
Suppose you have a channel with 1MHz bandwidth, that bandwidth set by a low-pass filter having time-constant of 160 nanoSeconds.

Now input a 2MHz datastream of alternating 1-0-1-0-1-0 pulses. This requires the pulses at the receiver recognize the level (the 1 or the 0) in 500 nanoSeconds.

The 500 nanoSeconds allows 3+ timeconstants of settling. Each Tau (time constant) improves the accuracy by one Neper, leaving a residual of 37% of the ideal final voltage. Thus 3+ Tau will have a residual of (0.37)^3 or 0.05.

If your data-slicer (the analog comparator threshold used to decide between 1 and 0 is at 50%, then the comparator will see either 0.95 or 0.05 at the end of each 500 nanosecond bittime.

In the absence of noise, this is a very reliable decision.

I think Shannon was including many other error sources in his theoretical prediction. 

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