ECE C392 Assignment # 1

Due Date Jan 27, 2001: Marks 20

Problem # 1

Consider a Parity check code that has 3 data bits and 4 parity check bits. Suppose that 3 of the code words are 1001011, 0101101 and 0011110. Find the rule for generating the parity checks. Find the set of all 8 code words. What is the minimum distance of the code ?

Problem # 2

Show that the final parity check in a horizontal and vertical parity check code, if taken as modulo 2 sum of all the data bits, is equal to the modulo sum of the horizontal parity checks and also equal to the modulo 2 sum of vertical parity checks

Problem # 3

Show that if g(D) contains the factor (1+D), then all error sequences with an odd number of errors are detected.

Problem # 4

Let g(D) = D4 + D2 + D + 1: s(D) = D3 + D + 1. Find Remainder when D4s (D) is divided by g(D), using modulo 2 arithmetic. By considering some other example of s(D) verify the error detection capabilities of this generator polynomial, using MATLAB code.