Our goal is to develop techniques to mitigate the

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Unformatted text preview: ent past were received incorrectly. Our goal is to develop techniques to mitigate the effects of both the BSC and burst errors. We’ll start with techniques that work well over a BSC and then discuss how to deal with bursts. A BSC error model is characterized by one number, p. We can determine p empirically by noting that if we send N bits over the channel, the expected number of erroneously 1 Graphical codes are sometimes also called “probabilistic codes” in the literature, for reasons we can’t get into here. 2 The “white” part of this term refers to the variance being the same over all the frequencies being used to communicate. SECTION 6.2. THE SIMPLEST CODE: REPLICATION 3 received bits is N · p. Hence, by sending a known bit pattern and counting the fraction or erroneously received bits, we can estimate p. In practice, even when BSC is a reasonable error model, the range of p could be rather large, between 10−2 (or even a bit higher) all the way to 10−10 or even 10−12 . A value of p of about 10−2 means that messages longer than a 100 bits will see at least one error on average; given that the typical unit of communication over a channel (a “packet”) is generally at le...
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