The ones marked pset are in the online problem set or

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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 | P0 D5 D6 D7 D8 D9 | P1 D10 D11 D12 D13 D14 | P2 ------------------------P3 P4 P5 P6 P7 | Her...
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