I guess low bandwidth is no problem. You only need to send a stream of price changes of the most common instruments (currencies, stocks). And only if there are meaningful movements. I guess a few kbit/s can already provide a lot of value. How fast would such a connection be? Is there an easy way to calculate the distance the signal takes compared to great circle line?
Wouldn't you just send whatever is needed to place the order? Do all of the processing at the source and just send the final instruction? (honest question I have no idea how this works)
Your trades only make money on the difference of the public information in London and what you get faster from Chicago. Therefore sending trade instructions isn't helpful as Chicago doesn't know London prices. But just giving the London algorithm that bit of inside can help a lot.
I assume trade strategies are mostly very simple as well. Basically just anticipating a change in price and quickly buying/selling to make some money off it.
N.B.: I only talk about Chicago->London here but given that Chicago hosts one of the largest Futures markets, I'd assume a lot is actually done in reverse. Using local prices from London of an underlying instrument (e.g. London stock market) to "predict" the value of the future traded in Chicago. You can make a lot of money if you know the price of the underlying instrument of a future before others do.