in (b) is indeed a linear block code by showing that it satisfies the two rules in (a). (d) Using trial and error (or any other method you can think of), find the generator matrix G that describes the linear block code. Verify that G is indeed the generator matrix by insuring that for every input m it satisfies u = mG (Q6.1) (f) Find the parity check matrix H, and show that GH = 0. (g) Build a syndrome table for correcting errors (a table with errors in one column and syndromes in the other). (h) Demonstrate (using your syndrome table) what happens when V=u+e= (0000)+(0001) enters the block coder. 4. Consider the 3-bit to 6-bit linear block coder described by generator matrix (Q6.2) Channel Coding and Decoding: Part 1-Block Coding and Decoding (a) Plot a table of input bits and output bits that describe the linear block coder. (b) Determine the parity check matrix H. (c) Create a syndrome table, with errors in one column and syndromes in the other. (d) Explain if and how the channel decoder corrects e = (001000). 5. Imagine you have a channel coder and decoder. In between them is a BPSK modulator with A = 1 and T = 2 an AWGN channel with No = 2 an optimal BPSK demodulator (Chapter 5) (a) What is the probability P that a bit error occurs at the BPSK demodulator? (b) If a rate 2/3 parity check bit channel coder/decoder is used, what is the probability that the channel coder fails to detect an error? (c) If a rate 4/9 rectangular code is used, determine the probability that you fail to correct an error. (d) Given a 3/6 linear block code with t = 1, find out how likely it is that it fails to correct an error. 6. Name a channel coder/decoder that can (a) Detect all 1 and 3 bit errors. (Explain.) (b) Detect all 1, 3, and 5 bit errors. (Explain.) (c) Correct all 1 bit errors in every 4 bits. (Explain.) (d) For (a), (b), and (c), provide an example of a received signal with an error on it, and show how the channel coder/decoder detects or corrects it. (e) Given the input bits 111000101001, provide the output bits for the