gle parity check bit coder, each set of k incoming bits is mapped to k + 1 outgoing bits. Take a look at Figure 6.3, which clearly explains what is going on. The additional bit is added to ensure that, if you added all the bits together, you would get a total of 0 (using modulo 2 addition: 0+0 0, 1+0 1, 0+1 = 1, 1+1 = 0). Channel coding where one bit is added to create a total sum of 0 is called even parity. You can Channel coder instead add one more bit SO that the total when adding all bits is 1, and this is called odd parity. You can decide add 1 bit which you like better, but to keep to ensure sum of things simple in this book, unless all bits is 0 otherwise stated, you can assume Figure 6.3 Single parity check bit coder I'm always referring to even parity. Channel Coding and Decoding: Part 1-Block Coding and Decoding Now we know what the channel coder does. What about the channel decoder? Using the example of Figure 6.3, the decoder takes the four bits received and adds them all together (modulo 2). If the total of the sum is 0, then it reports that there was no error detected. If the total happens to be 1, then it reports that in fact an error has occurred. For example, look at Figure 6.4. In Figure 6.4(a) you see the four transmitted bits. In Figure 6.4(b) you see the four received bits. Adding the received bits together modulo 2 you get a total of 1. Seeing that 1 tells you an error is detected. Let's see whether or not we can detect two errors with single parity check bits. In Figure 6.4(c), you see the received bits, with two errors in them. Adding all the re- ceived bits together, you get a sum of 0, which indicates "No error." But we know there are in fact two errors. So, single parity check bits can't be used to detect the case of two bit errors occurring. Actually, if you take a few minutes and look at different scenarios carefully, you'll find that a single parity check bit can always detect an odd number of errors, but can never detect an even number of errors. sum is O sum is 1 ERROR! bit in erro