a) Use the autoregressive model in Equation (8.40) with the flawed code word from Problem 8.6 to…

a) Use the autoregressive model in Equation (8.40) with the flawed code word from Problem 8.6 to find the location of each symbol error.

b) Find the value of each symbol error.

c) Use the information found in parts a) and b) to correct the flawed code word.

Problem 8.6

a) Suppose that the code word found in Problem 8.5 was degraded during transmission, so that its rightmost 6 bits are inverted. Find the value of each syndrome by evaluating the flawed code word polynomial at the roots of the generator polynomial g(X).

(b) Verify that the same syndrome values found in part a) can be found by evaluating the error polynomial, e(X), at the roots of g(X).

Problem 8.5

a) Use a LFSR to encode the symbols (6, 5, 1( (rightmost symbol is the earliest) with a (7, 3) R-S code in systematic form. Show the resulting code word in binary form. b) Verify the encoding results from part a) by evaluating the code word polynomial at the roots of the (7, 3) R-S generator polynomial, g(X).