Question 8 (carries 15 marks)
The generator polynomial g(r) of a (7,4) systematic cyclic code is given by g(x) = 1 + x + x^3.
(a) Use this encoder to find the codewords for the following messages by filling in Table Q8.
Table Q8
Message | Codeword
1000 | 0100 0010
000 | 0001
(b) Using your result in (a), find the generator matrix G and parity check matrix H of the code.
(c) What is the error-correcting capability of this code?
(d) Find all the syndromes of single-bit error patterns.
(e) Decode the received sequence LOOOI4_.
(f) Explain why it is sometimes better to detect errors instead of correcting errors.