We will discuss how to produce such embeddings in the

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Unformatted text preview: ce, if our goal is to detect errors, we can use an embedding of the set of messages we wish to transmit into a bigger space, so that the minimum Hamming distance between any two code words in the bigger space is at least one more than the number of errors we wish to detect. (We will discuss how to produce such embeddings in the subsequent sections.) But what about the problem of correcting errors? Let’s go back to Figure 6-2, with S = {00, 11}. Suppose the receiver receives 01. It can tell that a single error has occurred, but it can’t tell whether the correct data sent was 00 or 11—both those possible patterns are equally likely under the BSC error model. 6 LECTURE 6. COPING WITH BIT ERRORS Figure 6-2: Code words separated by a Hamming distance of 2 can be used to detect single bit errors. The code words are shaded in each picture. The picture on the left is a (2,1) repetition code, which maps 1-bit messages to 2-bit code words. The code on the right is a (3,2) code, which maps 2-bit messages to 3-bit code words. Ah, but we ca...
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