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Unformatted text preview: set of “ﬁrst” bits, or a
set of “second” bits, or a set of “third” bits, etc., because those are the bits sent in order on
the channel. As long as only a set of k th bits are corrupted, the receiver can correct all the
errors. The reason is that each coded block will now have at most one error. Thus, SEC
codes are a useful primitive to correct against burst errors, in concert with interleaving. Acknowledgments Many thanks to Katrina LaCurts for carefully reading these notes and making several useful comments. SECTION 6.5. PROTECTING LONGER MESSAGES WITH SEC CODES 17 Problems and Questions These questions are to help you improve your understanding of the concepts discussed in
this lecture. The ones marked *PSet* are in the online problem set or lab.
1. Show that the Hamming distance satisﬁes the triangle inequality. That is, show that
HD(x, y ) + HD(y, z ) ≥ HD(x, z ) for any three n-bit binary numbers in F2 .
2. Consider the following rectangular linear block code:
D0 D1 D2 D3 D4
D5 D6 D7 D8 D9
D10 D11 D12 D13 D14 | P2
------------------------P3 P4 P5 P6 P7
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- Fall '13