Error Correcting Codes
نویسنده
چکیده
Error correcting codes make possible much of digital technology, from modems to cell phones to compact disk players. The problem is to send a message across a noisy channel with perfect fidelity, or at least with as much fidelity as possible. Below we will describe the theory of these codes. It is based on some ideas from “modern algebra,” including finite number systems called rings and fields. We’ll learn about these, but let’s first think about digital messages. Whether they represent a newspaper article, a musical performance, a conversation, or a painting, they consists of a sequence of 0’s and 1’s. A message might look like this: 011010110010 ... (1) However, noise can change bits of information: some 0’s might get changed to 1’s and vice versa as the message moves from sender to receiver. Thus the above message might be received as
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