Fitch cheney's five card trick | Mathematics

In 1950 mathematician and magician William Fitch Cheney Jr. published a two-person card trick. Some consider it the best mathematical card trick ever devised. The basic effect is as follows.
Five cards are randomly picked from a deck (can be a borrowed deck, an incomplete deck ... there is nothing marked or otherwise tricky with the deck) and given to the performer, who shows four of them to his performing partner. The partner sees nothing else except the four cards (no other signaling or silent codes), but promptly reveals the identity of the fifth card.
Obviously the identity of the 5th card has to be transmitted with the four cards. But how?