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Math Help - Coding theory question

  1. #1
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    Coding theory question

    an error correction encoding/decoding system for storing 4 digit binary sequences is set up using a 5-frame delay cross-interleave of two codes C_{1} and C_{2}. The code C_{1} has length 7, distance 3 and has the 4 digit binary strings as the message words for the code. The code C_{2} is the first-order Reed-Muller code R(6). The data is stored as a sequence of binary digits on the tape with no alteration (eg modulation) other than the error correction encoding.

    (a) The system must be designed so that for some interger r, received words which are distance r or greater from a C_{2} codeword have all their symbls marked as erasures. Received words at distance less than r must be corrected by the C_{2}decoder and the number of errors which the C_{2}decoder corrects must be maximised. However, it is also required that the chance of a random received word (which is a random sequence of 64 binary digits as a result of a burst error) being
    undetected by the
    R(6)" alt="R(6)" /> decoder is less than 1 10^-11" alt="10^-11" />. Find r.


    (b)
    Determine the smallest integer t such that there is a burst error of length t that the system cannot correct (in the presence of no other errors).

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  2. #2
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    sorry the last part of (a) should read:

    being undetected by the R(6) decoder is less than 1 x 10^-11. Find r.
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  3. #3
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    Quote Originally Posted by wik_chick88 View Post
    sorry the last part of (a) should read:

    being undetected by the R(6) decoder is less than 1 x 10^-11. Find r.

    grrr its 1 x 10^(-11)
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  4. #4
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    Quote Originally Posted by wik_chick88 View Post
    grrr its 1 x 10^(-11)
    nope its 10^{-11}
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