![]() ![]() Shannon showed that, statistically, if you consider all possible assignments of random codes to messages, there must be at least one that approaches the Shannon limit. But of the 16 permitted codes, there’s likely to be only one that best fits the received sequence - that differs, say, by only a digit. If the receiver receives one of those 240 sequences, she knows that an error has crept into the data. Since there are 256 possible sequences of eight bits, there are at least 240 that don’t appear in the codebook. The receiver, like the sender, would have a codebook that correlates the 16 possible four-bit messages with 16 eight-bit codes. Shannon’s proof would assign each of them its own randomly selected code - basically, its own serial number.Ĭonsider the case in which the channel is noisy enough that a four-bit message requires an eight-bit code. Say you want to send a single four-bit message over a noisy channel. His proof, however, didn’t explain how to construct such a code. In fact, he was able to prove that for any communications channel, there must be an error-correcting code that enables transmissions to approach the Shannon limit. It cuts the data transmission rate by two-thirds, since it requires three times as many bits per message, but it’s still very vulnerable to error: two errors in the right places would make the original message unrecoverable.īut Shannon knew that better error-correcting codes were possible. So the ideal code would minimize the number of extra bits while maximizing the chance of correcting error.īy that standard, sending a message three times is actually a terrible code. As codes get longer, however, the transmission rate goes down: you need more bits to send the same fundamental message. The noisier the channel, the more information you need to add to compensate for errors. If an error crept in, and the receiver received 001011001 instead, she could be reasonably sure that the correct string was 001.Īny such method of adding extra information to a message so that errors can be corrected is referred to as an error-correcting code. For instance, if you were trying to transmit a message with only three bits, like 001, you could send it three times: 001001001. ![]() In a noisy channel, the only way to approach zero error is to add some redundancy to a transmission. He called that rate the channel capacity, but today, it’s just as often called the Shannon limit. Given a channel with particular bandwidth and noise characteristics, Shannon showed how to calculate the maximum rate at which data can be sent over it with zero error. Bandwidth is the range of electronic, optical or electromagnetic frequencies that can be used to transmit a signal noise is anything that can disturb that signal. Shannon, who taught at MIT from 1956 until his retirement in 1978, showed that any communications channel - a telephone line, a radio band, a fiber-optic cable - could be characterized by two factors: bandwidth and noise. “People who know Shannon’s work throughout science think it’s just one of the most brilliant things they’ve ever seen,” says David Forney, an adjunct professor in MIT’s Laboratory for Information and Decision Systems. They’d been supplied in 1948 by Claude Shannon SM ’37, PhD ’40 in a groundbreaking paper that essentially created the discipline of information theory. In fact, by the early 1980s, the answers to the first two questions were more than 30 years old. ![]() Are there codes that can drive the data rate even higher? If so, how much higher? And what are those codes? Then a group of engineers demonstrates that newly devised error-correcting codes can boost a modem’s transmission rate by 25 percent. For years, modems that send data over the telephone lines have been stuck at a maximum rate of 9.6 kilobits per second: if you try to increase the rate, an intolerable number of errors creeps into the data. It’s the early 1980s, and you’re an equipment manufacturer for the fledgling personal-computer market. ![]()
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