If two codewords are a Hamming distanceIf two codewords are a Hamming distance dd apart, it willapart, it willrequirerequire dd singlesingle--bit errors to convert one into the other.bit errors to conve
Question
If two codewords are a Hamming distanceIf two codewords are a Hamming distance dd apart, it willapart, it willrequirerequire dd singlesingle--bit errors to convert one into the other.bit errors to conve
Solution
If two codewords are a Hamming distance dd apart, it will require dd single-bit errors to convert one into the other.
To understand this statement, let's break it down step by step:
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Hamming distance: The Hamming distance between two codewords is the number of positions at which the corresponding bits are different. In other words, it measures the minimum number of bit flips required to transform one codeword into another.
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dd apart: When we say two codewords are "dd apart," it means their Hamming distance is equal to dd. So, there are exactly dd positions where the bits differ between the two codewords.
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Single-bit errors: A single-bit error refers to a situation where only one bit in a codeword is flipped or changed. In other words, it is a single bit that is in an incorrect state compared to the original codeword.
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Converting one codeword into the other: To convert one codeword into another, we need to perform a series of bit flips or single-bit errors. The number of single-bit errors required to transform one codeword into another is equal to the Hamming distance between them.
Therefore, if two codewords are a Hamming distance dd apart, it will require dd single-bit errors to convert one into the other.
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