Keeping the Noise Down
Shannon used mathematics to find the optimal way to combat noise during transmission of communication signals. Shannon was able to define the entropy and the equivocation of signals using statistical formulas, and then to use these measurements to determine the capacity of a given communication channel. In data transmission, entropy is a measure of the loss of information in a transmitted signal or message.2 Equivocation is the average ambiguity of the received signal. Shannon calculated channel capacity by finding the maximum difference the entropy and the equivocation of a signal in a communication system. He represented this formulaically with the following:
This formula builds on the formula shown in "Communication Systems" because it accounts for noise. The formula in "Communication Systems" looks like this:
Shannon wrote this formula to measure channel capacity in a communication system without noise.
Shannon delivered a talk entitled "Game Playing Machines" at the 1955 Medal Day proceedings at The Franklin Institute. You can read the letters he sent to The Franklin Institute expressing his willingness to speak at Medal Day, as well as his Medal Day itinerary, by clicking on the thumbnails at right.
2 http://dictionary.reference.com/browse/entropy (Dictionary.com)
Letter to Shannon from Allen, (314k);
Letter to Allen from Shannon, (340k);
Letter to Dr. Claude E. Shannon, Bell Telephone Laboratories, from Henry B. Allen, Executive Vice President of The Franklin Institute / (451k);