 = 2k = 2 bits. A picture will make this much clearer, SO take a look at Figure 7.2. The arrow on the left shows where the bits come in. With k = 1, bits come in one bit at a time. The box with lines that the k = 1 bit walks into is meant to represent a 3-bit shift register. Chapter Seven Convolutional 101111 Coder remembers Block of Block of n=6 k= 3 bits 110 111 bits output comes in Previous K= 2 sets of k=3 bits. Uses this plus input to determine output. Figure 7.1 Convolutional coder idea Convolutional coder Block of Block of k=1 bit n= 2 bits comes in comes out stores holds current K = 2 incoming previous bit sets of k= 1 bit Figure 7.2 Example of convolutional coder Channel Coding and Decoding: Part 2-Convolutional Coding and Decoding When the 1 bit comes in, it is stored in the position labeled "1." It moves the bit that was in position 1 over to position 2, and what is in position 2 over to position 3. Now, we know what is happening to the inputs, but what about the outputs? You can see two adders, one at the top of the picture and one at the bottom. The top adder takes all three bits in the shift register, adds them together (modulo 2), and uses that to create the first bit of the output. The bottom adder takes the first and third bits, adds them together (modulo 2), and this forms the second bit of the output. The switch at the very right is meant to show the conversion of the two output bits from parallel form to serial form. In this way, k= 1 bit comes in, and using this one bit and the K = 2 previous bits, two output bits are created. We get one bit in, two bits out, and this is a convolutional coder. 7.1.2 Making Sure We've Got It Figure 7.3 shows a simple example describing the workings of the convolutional channel coder in Figure 7.2. The bits coming in are 1, then 0, then 100. Let's together figure out what is coming out of the convolutional coder given this input. At time 0, before things get started, we have all Os in the shift register. Now, let's move to time 1, when bit 1 comes in, and see w