Shannon's Way

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In a 1939 letter to his mentor, Vannevar Bush, Shannon outlined some of his initial ideas on “fundamental properties of general systems for the transmission of intelligence. The tranquility along this trail is so special and under foot the trail is within the natural area of focus. If the sequences were equally likely, then Shannon’s formula would say that the entropy rate is indeed 470 bits per minute. Repeating a message is an example of using a code to transmit a message, and by using different and more sophisticated codes, one can communicate fast — all the way up to the speed limit, C — while maintaining any given degree of reliability. Finally, he showed that reliable communication of the information from the source in the face of noise is possible if and only if H< C.

But over my career, as I had the opportunity to apply this philosophy in my own work, I began to understand. The lower the entropy rate, the less the uncertainty, and thus the easier it is to compress the message into something shorter.Shannon’s general theory of communication is so natural that it’s as if he discovered the universe’s laws of communication, rather than inventing them. Thus, information is like water: If the flow rate is less than the capacity of the pipe, then the stream gets through reliably.

So in a radio system, for example, even though both the initial sound and the electromagnetic signal sent over the air are analog wave forms, Shannon’s theorems imply that it is optimal to first digitize the sound wave into bits, and then map those bits into the electromagnetic wave.

Indeed, the 5G standard currently rolling out uses not one but two practical codes proved to achieve Shannon’s speed limit. An earlier version of this article incorrectly stated the rate of text messages possible if sending 100 letters per minute. By using the Web site, you confirm that you have read, understood, and agreed to be bound by the Terms and Conditions.

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