pter Six output bits from input bits, because in this case all you have to store is G, and that is only n.k bits. Let's see if this really works, rather than just taking my word for it. Consider the generator matrix G corresponding to 110100 G = 011010 (6.2) 101001 This is the generator matrix for the (6,3) code seen in Figure 6.10. Let's say the input is m = (101). Then the output is (6.3) 110100 =(101) 011010 (6.4) 101001 = (011101) (6.5) If we compare that to the output we expect from the look-up table of Figure 6.9, then we see we've got a match. input to linear block coder output of linear block coder Figure 6.10 last 3 bits of output Systematic linear block codes =3 input bits Channel Coding and Decoding: Part 1-Block Coding and Decoding 6.2.3 Systematic Linear Block Codes Look at Figure 6.10 again, which shows the input and the output of a linear block coder. Specifically, take a look at the right side of this figure, which shows the output. Look carefully at the last three bits of the block coder output, and note that the last three bits in the output 6-bit set match the 3 input bits. Not all linear block codes satisfy this property, but if they happen to, they are called systematic linear block codes. People-mostly engineers-like to use systematic linear block codes because it helps them save memory. First, recall that for linear block codes you can get the channel coder output by applying the simple equation (6.6) If you know that the last bits of the output match the input bits, then you can easily show that G will look like (for the case of 3-bit sets mapped to 6-bit sets) G=(P3x3:13x) (6.7) = P21 P22 P23 010 (6.8) P31 P32 P33 0 0 1 That means all you need to store in the memory of the channel coder is the matrix P. It will be made up of k(n-k) elements that are either 0 or 1, SO it really won't require a lot of memory to store it. That is about all there is to know about channel coding for block codes. There really is only one rule that makes a block code a linear block code, and it's only six words 