(7,3) CRC Codes

Discussion in 'Homework Help' started by ||Steve||, May 8, 2013.

  1. ||Steve||

    Thread Starter New Member

    Dec 18, 2009
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    0
    Not sure if this is the correct place for this question. It's a comms question though so hopefully relevant.

    I have a question that goes as follows:

    Question:

    When generating a (7,3) cyclic block cyclic using the Generator polynomial G(X) = 1 + x^2 + x^3 + x^4

    (i) Derive a table of valid codewords(ii) Draw the block diagram of a suitable linear shift register decoding circuit for the above code and indicate how the circuit would function
    ...
    (iv) If the codeword 1 + x + x^5 + x^5 is received, what codeword was sent.


    Problem:
    My problem is the fact that this is a (7,3) code rather than a (7,4) code. I know how to work with (7,4) codes and I'm comfortable with generating the checksums. However, I'm not sure what changes as a result of the extra check bit. I fear either my circuit (below - answer to part ii) or my table of codewords is wrong (also below - answer to part i). This isn't helped by the fact that I can't match any of the codes to the one given in part (iii)

    Code ( (Unknown Language)):
    1.  
    2. [U][B][I]The table:[/I][/B][/U]
    3.  
    4. [FONT=Courier New][B]Datablock     Code Polynomials     Code Values
    5. =========     ================     ===========[/B]
    6. 000           (0) * g(x)            0000000
    7. 001           (1) * g(x)            0011101
    8. 010           (x) * g(x)            0111010
    9. 011           (1+x) * g(x)          1010111
    10. 100           (x2) * g(x)           1110100
    11. 101           (1+x2) * g(x)        10010001
    12. 110           [/FONT][FONT=Courier New][FONT=Courier New](x+x2) * g(x)        10101110
    13. [/FONT]111           (1+x+x2) * g(x)      11001011
    14. [/FONT]
    15. [I][U][B]The circuit:[/B][/U][/I]
    16.  
    (Input at left)
    ATTACHED
    [​IMG]
     
    Last edited by a moderator: May 8, 2013
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