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Unformatted text preview: drome equations for E0 , E1 , E2 .
(c) For the eight possible syndrome values, determine what error can be detected
(none, error in a particular data or parity bit, or multiple errors). Make your
choice using maximum likelihood decoding, assuming a small bit error probability (i.e., the smallest number of errors that’s consistent with the given syndrome).
(d) Suppose that the the 5-bit blocks arrive at the receiver in the following order:
D0 , D1 , P0 , P1 , P2 . If 11011 arrives, what will the TBC receiver report as the received data after error correction has been performed? Explain your answer. 18 LECTURE 6. COPING WITH BIT ERRORS (e) TBC would like to improve the code rate while still maintaining single-bit error
correction. Their engineer would like to reduce the number of parity bits by 1.
Give the formulas for P0 and P1 that will accomplish this goal, or brieﬂy explain
why no such code is possible.
5. For any linear block code over F2 with minimum Hamming distance at least 2t + 1
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- Fall '13