# (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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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

• ###### shift_reg_crc.PNG
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Last edited by a moderator: May 8, 2013